Edit 2018: This answer is pretty old and it uses checks for old browsers that are not necessary anymore, as the clientX and clientY properties work in all current browsers. You might want to check out Patriques Answer for a simpler, more recent solution.

Original Answer:
As described in an article i found back then but exists no longer:

var x;
var y;
if (e.pageX || e.pageY) { 
  x = e.pageX;
  y = e.pageY;
}
else { 
  x = e.clientX + document.body.scrollLeft + document.documentElement.scrollLeft; 
  y = e.clientY + document.body.scrollTop + document.documentElement.scrollTop; 
} 
x -= gCanvasElement.offsetLeft;
y -= gCanvasElement.offsetTop;

Worked perfectly fine for me.

So this is both simple but a slightly more complicated topic than it seems.

First off there are usually to conflated questions here

1. How to get element relative mouse coordinates

2. How to get canvas pixel mouse coordinates for the 2D Canvas API or WebGL

so, answers

How to get element relative mouse coordinates

Whether or not the element is a canvas getting element relative mouse coordinates is the same for all elements.

There are 2 simple answers to the question "How to get canvas relative mouse coordinates"

Simple answer #1 use offsetX and offsetY

canvas.addEventListner('mousemove', (e) => {
  const x = e.offsetX;
  const y = e.offsetY;
});

This answer works in Chrome, Firefox, and Safari. Unlike all the other event values offsetX and offsetY take CSS transforms into account.

The biggest problem with offsetX and offsetY is as of 2019/05 they don't exist on touch events and so can't be used with iOS Safari. They do exist on Pointer Events which exist in Chrome and Firefox but not Safari although apparently Safari is working on it.

Another issue is the events must be on the canvas itself. If you put them on some other element or the window you can not later choose the canvas to be your point of reference.

Simple answer #2 use clientX, clientY and canvas.getBoundingClientRect

If you don't care about CSS transforms the next simplest answer is to call canvas. getBoundingClientRect() and subtract the left from clientX and top from clientY as in

canvas.addEventListener('mousemove', (e) => {
  const rect = canvas.getBoundingClientRect();
  const x = e.clientX - rect.left;
  const y = e.clientY - rect.top;
});

This will work as long as there are no CSS transforms. It also works with touch events and so will work with Safari iOS

canvas.addEventListener('touchmove', (e) => {
  const rect = canvas. getBoundingClientRect();
  const x = e.touches[0].clientX - rect.left;
  const y = e.touches[0].clientY - rect.top;
});

How to get canvas pixel mouse coordinates for the 2D Canvas API

For this we need to take the values we got above and convert from the size the canvas is displayed to the number of pixels in the canvas itself

with canvas.getBoundingClientRect and clientX and clientY

canvas.addEventListener('mousemove', (e) => {
  const rect = canvas.getBoundingClientRect();
  const elementRelativeX = e.clientX - rect.left;
  const elementRelativeY = e.clientY - rect.top;
  const canvasRelativeX = elementRelativeX * canvas.width / rect.width;
  const canvasRelativeY = elementRelativeY * canvas.height / rect.height;
});

or with offsetX and offsetY

canvas.addEventListener('mousemove', (e) => {
  const elementRelativeX = e.offsetX;
  const elementRelativeY = e.offsetY;
  const canvasRelativeX = elementRelativeX * canvas.width / canvas.clientWidth;
  const canvasRelativeY = elementRelativeY * canvas.height / canvas.clientHeight;
});

Note: In all cases do not add padding or borders to the canvas. Doing so will massively complicate the code. Instead of you want a border or padding surround the canvas in some other element and add the padding and or border to the outer element.

Working example using event.offsetX, event.offsetY

[...document.querySelectorAll('canvas')].forEach((canvas) => {
  const ctx = canvas.getContext('2d');
  ctx.canvas.width  = ctx.canvas.clientWidth;
  ctx.canvas.height = ctx.canvas.clientHeight;
  let count = 0;

  function draw(e, radius = 1) {
    const pos = {
      x: e.offsetX * canvas.width  / canvas.clientWidth,
      y: e.offsetY * canvas.height / canvas.clientHeight,
    };
    document.querySelector('#debug').textContent = count;
    ctx.beginPath();
    ctx.arc(pos.x, pos.y, radius, 0, Math.PI * 2);
    ctx.fillStyle = hsl((count++ % 100) / 100, 1, 0.5);
    ctx.fill();
  }

  function preventDefault(e) {
    e.preventDefault();
  }

  if (window.PointerEvent) {
    canvas.addEventListener('pointermove', (e) => {
      draw(e, Math.max(Math.max(e.width, e.height) / 2, 1));
    });
    canvas.addEventListener('touchstart', preventDefault, {passive: false});
    canvas.addEventListener('touchmove', preventDefault, {passive: false});
  } else {
    canvas.addEventListener('mousemove', draw);
    canvas.addEventListener('mousedown', preventDefault);
  }
});

function hsl(h, s, l) {
  return `hsl(${h * 360 | 0},${s * 100 | 0}%,${l * 100 | 0}%)`;
}

.scene {
  width: 200px;
  height: 200px;
  perspective: 600px;
}

.cube {
  width: 100%;
  height: 100%;
  position: relative;
  transform-style: preserve-3d;
  animation-duration: 16s;
  animation-name: rotate;
  animation-iteration-count: infinite;
  animation-timing-function: linear;
}

@keyframes rotate {
  from { transform: translateZ(-100px) rotateX(  0deg) rotateY(  0deg); }
  to   { transform: translateZ(-100px) rotateX(360deg) rotateY(720deg); }
}

.cube__face {
  position: absolute;
  width: 200px;
  height: 200px;
  display: block;
}

.cube__face--front  { background: rgba(255, 0, 0, 0.2); transform: rotateY(  0deg) translateZ(100px); }
.cube__face--right  { background: rgba(0, 255, 0, 0.2); transform: rotateY( 90deg) translateZ(100px); }
.cube__face--back   { background: rgba(0, 0, 255, 0.2); transform: rotateY(180deg) translateZ(100px); }
.cube__face--left   { background: rgba(255, 255, 0, 0.2); transform: rotateY(-90deg) translateZ(100px); }
.cube__face--top    { background: rgba(0, 255, 255, 0.2); transform: rotateX( 90deg) translateZ(100px); }
.cube__face--bottom { background: rgba(255, 0, 255, 0.2); transform: rotateX(-90deg) translateZ(100px); }

<div class="scene">
  <div class="cube">
    <canvas class="cube__face cube__face--front"></canvas>
    <canvas class="cube__face cube__face--back"></canvas>
    <canvas class="cube__face cube__face--right"></canvas>
    <canvas class="cube__face cube__face--left"></canvas>
    <canvas class="cube__face cube__face--top"></canvas>
    <canvas class="cube__face cube__face--bottom"></canvas>
  </div>
</div>
<pre id="debug"></pre>

Working example using canvas.getBoundingClientRect and event.clientX and event.clientY

const canvas = document.querySelector('canvas');
const ctx = canvas.getContext('2d');
ctx.canvas.width  = ctx.canvas.clientWidth;
ctx.canvas.height = ctx.canvas.clientHeight;
let count = 0;

function draw(e, radius = 1) {
  const rect = canvas.getBoundingClientRect();
  const pos = {
    x: (e.clientX - rect.left) * canvas.width  / canvas.clientWidth,
    y: (e.clientY - rect.top) * canvas.height / canvas.clientHeight,
  };
  ctx.beginPath();
  ctx.arc(pos.x, pos.y, radius, 0, Math.PI * 2);
  ctx.fillStyle = hsl((count++ % 100) / 100, 1, 0.5);
  ctx.fill();
}

function preventDefault(e) {
  e.preventDefault();
}

if (window.PointerEvent) {
  canvas.addEventListener('pointermove', (e) => {
    draw(e, Math.max(Math.max(e.width, e.height) / 2, 1));
  });
  canvas.addEventListener('touchstart', preventDefault, {passive: false});
  canvas.addEventListener('touchmove', preventDefault, {passive: false});
} else {
  canvas.addEventListener('mousemove', draw);
  canvas.addEventListener('mousedown', preventDefault);
}

function hsl(h, s, l) {
  return `hsl(${h * 360 | 0},${s * 100 | 0}%,${l * 100 | 0}%)`;
}

canvas { background: #FED; }

<canvas width="400" height="100" style="width: 300px; height: 200px"></canvas>
<div>canvas deliberately has differnt CSS size vs drawingbuffer size</div>

Here is a small modification to Ryan Artecona's answer for canvases with a variable (%) width:

 HTMLCanvasElement.prototype.relMouseCoords = function (event) {
    var totalOffsetX = 0;
    var totalOffsetY = 0;
    var canvasX = 0;
    var canvasY = 0;
    var currentElement = this;

    do {
        totalOffsetX += currentElement.offsetLeft;
        totalOffsetY += currentElement.offsetTop;
    }
    while (currentElement = currentElement.offsetParent)

    canvasX = event.pageX - totalOffsetX;
    canvasY = event.pageY - totalOffsetY;

    // Fix for variable canvas width
    canvasX = Math.round( canvasX * (this.width / this.offsetWidth) );
    canvasY = Math.round( canvasY * (this.height / this.offsetHeight) );

    return {x:canvasX, y:canvasY}
}

See demo at http://jsbin.com/ApuJOSA/1/edit?html,output .

  function mousePositionOnCanvas(e) {
      var el=e.target, c=el;
      var scaleX = c.width/c.offsetWidth || 1;
      var scaleY = c.height/c.offsetHeight || 1;

      if (!isNaN(e.offsetX)) 
          return { x:e.offsetX*scaleX, y:e.offsetY*scaleY };

      var x=e.pageX, y=e.pageY;
      do {
        x -= el.offsetLeft;
        y -= el.offsetTop;
        el = el.offsetParent;
      } while (el);
      return { x: x*scaleX, y: y*scaleY };
  }

I was creating an application having a canvas over a pdf, that involved a lot of resizes of canvas like Zooming the pdf-in and out, and in turn on every zoom-in/out of PDF I had to resize the canvas to adapt the size of the pdf, I went through lot of answers in stackOverflow, and didn't found a perfect solution that will eventually solve the problem.

I was using rxjs and angular 6, and didn't found any answer specific to the newest version.

Here is the entire code snippet that would be helpful, to anyone leveraging rxjs to draw on top of canvas.

  private captureEvents(canvasEl: HTMLCanvasElement) {

    this.drawingSubscription = fromEvent(canvasEl, 'mousedown')
      .pipe(
        switchMap((e: any) => {

          return fromEvent(canvasEl, 'mousemove')
            .pipe(
              takeUntil(fromEvent(canvasEl, 'mouseup').do((event: WheelEvent) => {
                const prevPos = {
                  x: null,
                  y: null
                };
              })),

              takeUntil(fromEvent(canvasEl, 'mouseleave')),
              pairwise()
            )
        })
      )
      .subscribe((res: [MouseEvent, MouseEvent]) => {
        const rect = this.cx.canvas.getBoundingClientRect();
        const prevPos = {
          x: Math.floor( ( res[0].clientX - rect.left ) / ( rect.right - rect.left ) * this.cx.canvas.width ),
          y:  Math.floor( ( res[0].clientY - rect.top ) / ( rect.bottom - rect.top ) * this.cx.canvas.height )
        };
        const currentPos = {
          x: Math.floor( ( res[1].clientX - rect.left ) / ( rect.right - rect.left ) * this.cx.canvas.width ),
          y: Math.floor( ( res[1].clientY - rect.top ) / ( rect.bottom - rect.top ) * this.cx.canvas.height )
        };

        this.coordinatesArray[this.file.current_slide - 1].push(prevPos);
        this.drawOnCanvas(prevPos, currentPos);
      });
  }

And here is the snippet that fixes, mouse coordinates relative to size of the canvas, irrespective of how you zoom-in/out the canvas.

const prevPos = {
  x: Math.floor( ( res[0].clientX - rect.left ) / ( rect.right - rect.left ) * this.cx.canvas.width ),
  y:  Math.floor( ( res[0].clientY - rect.top ) / ( rect.bottom - rect.top ) * this.cx.canvas.height )
};
const currentPos = {
  x: Math.floor( ( res[1].clientX - rect.left ) / ( rect.right - rect.left ) * this.cx.canvas.width ),
  y: Math.floor( ( res[1].clientY - rect.top ) / ( rect.bottom - rect.top ) * this.cx.canvas.height )
};

Here is a simplified solution (this doesn't work with borders/scrolling):

function click(event) {
    const bound = event.target.getBoundingClientRect();

    const xMult = bound.width / can.width;
    const yMult = bound.height / can.height;

    return {
        x: Math.floor(event.offsetX / xMult),
        y: Math.floor(event.offsetY / yMult),
    };
}

Hey, this is in dojo, just cause it's what I had the code in already for a project.

It should be fairly Obvious how to convert it back to non dojo vanilla JavaScript.

  function onMouseClick(e) {
      var x = e.clientX;
      var y = e.clientY;
  }
  var canvas = dojo.byId(canvasId);
  dojo.connect(canvas,"click",onMouseClick);

Hope that helps.