I did some more work on these extensions - You can find the code here

I wrote some extension methods that extend System.Enum that I use often... I'm not claiming that they are bulletproof, but they have helped... Comments removed...

namespace Enum.Extensions {

    public static class EnumerationExtensions {

        public static bool Has<T>(this System.Enum type, T value) {
            try {
                return (((int)(object)type & (int)(object)value) == (int)(object)value);
            } 
            catch {
                return false;
            }
        }

        public static bool Is<T>(this System.Enum type, T value) {
            try {
                return (int)(object)type == (int)(object)value;
            }
            catch {
                return false;
            }    
        }


        public static T Add<T>(this System.Enum type, T value) {
            try {
                return (T)(object)(((int)(object)type | (int)(object)value));
            }
            catch(Exception ex) {
                throw new ArgumentException(
                    string.Format(
                        "Could not append value from enumerated type '{0}'.",
                        typeof(T).Name
                        ), ex);
            }    
        }


        public static T Remove<T>(this System.Enum type, T value) {
            try {
                return (T)(object)(((int)(object)type & ~(int)(object)value));
            }
            catch (Exception ex) {
                throw new ArgumentException(
                    string.Format(
                        "Could not remove value from enumerated type '{0}'.",
                        typeof(T).Name
                        ), ex);
            }  
        }

    }
}

Then they are used like the following

SomeType value = SomeType.Grapes;
bool isGrapes = value.Is(SomeType.Grapes); //true
bool hasGrapes = value.Has(SomeType.Grapes); //true

value = value.Add(SomeType.Oranges);
value = value.Add(SomeType.Apples);
value = value.Remove(SomeType.Grapes);

bool hasOranges = value.Has(SomeType.Oranges); //true
bool isApples = value.Is(SomeType.Apples); //false
bool hasGrapes = value.Has(SomeType.Grapes); //false

The idiom is to use the bitwise or-equal operator to set bits:

flags |= 0x04;

To clear a bit, the idiom is to use bitwise and with negation:

flags &= ~0x04;

Sometimes you have an offset that identifies your bit, and then the idiom is to use these combined with left-shift:

flags |= 1 << offset;
flags &= ~(1 << offset);

C++ syntax, assuming bit 0 is LSB, assuming flags is unsigned long:

Check if Set:

flags & (1UL << (bit to test# - 1))

Check if not set:

invert test !(flag & (...))

Set:

flag |= (1UL << (bit to set# - 1))

Clear:

flag &= ~(1UL << (bit to clear# - 1))

Toggle:

flag ^= (1UL << (bit to set# - 1))

For the best performance and zero garbage, use this:

using System;
using T = MyNamespace.MyFlags;

namespace MyNamespace
{
    [Flags]
    public enum MyFlags
    {
        None = 0,
        Flag1 = 1,
        Flag2 = 2
    }

    static class MyFlagsEx
    {
        public static bool Has(this T type, T value)
        {
            return (type & value) == value;
        }

        public static bool Is(this T type, T value)
        {
            return type == value;
        }

        public static T Add(this T type, T value)
        {
            return type | value;
        }

        public static T Remove(this T type, T value)
        {
            return type & ~value;
        }
    }
}

Bitwise (Flags) enum guide

Old, but wanted to take a stab at a cheat sheet, even if for my own reference:

Examples

[Flags]
enum E {
    A = 0b1,
    B = 0b10,
    C = 0b100
}

E e = E.A;        // Assign (e = A)
e |= E.B | E.C;   // Add    (e = A, B, C)
e &= ~E.A & ~E.B; // Remove (e = C) -- alt syntax: &= ~(E.A | E.B)
e ^= E.A | E.C;   // Toggle (e = A)
e.HasFlag(E.A);   // Test   (returns true)

// Testing multiple flags using bit operations:
bool hasAandB = ( e & (E.A | E.B) ) == (E.A | E.B);

Bonus: defining a Flags enum

Typically, we use integers like so:

[Flags]
enum E {
    A = 1,
    B = 2,
    C = 4,
    // etc.

But as we approach larger numbers, it's not as easy to calculate the next value:

  // ...
  W = 4194304,
  X = 8388608,
  // ..

There are a couple of alternatives, however: binary and hexadecimal literals.

For Binary, just append a 0 at the end of the previous value:

[Flags]
enum E {
    A = 0b1,
    B = 0b10,
    C = 0b100,
    // ...
    W = 0b100_0000_0000_0000_0000_0000,
    X = 0b1000_0000_0000_0000_0000_0000,

Hexadecimal also has a handy pattern and might look a bit less ugly: cycle through 1, 2, 4, 8, adding a zero after each complete iteration.

[Flags]
enum E {
    A = 0x1,
    B = 0x2,
    C = 0x4,
    D = 0x8,
    E = 0x10, // 16
    F = 0x20, // 32, etc.
    // ...
    W = 0x400000,
    X = 0x800000,

To test a bit you would do the following: (assuming flags is a 32 bit number)

Test Bit:

if((flags & 0x08) == 0x08)

flags = flags ^ 0x08;

flags = flags & 0xFFFFFF7F;

This was inspired by using Sets as indexers in Delphi, way back when:

/// Example of using a Boolean indexed property
/// to manipulate a [Flags] enum:

public class BindingFlagsIndexer
{
  BindingFlags flags = BindingFlags.Default;

  public BindingFlagsIndexer()
  {
  }

  public BindingFlagsIndexer( BindingFlags value )
  {
     this.flags = value;
  }

  public bool this[BindingFlags index]
  {
    get
    {
      return (this.flags & index) == index;
    }
    set( bool value )
    {
      if( value )
        this.flags |= index;
      else
        this.flags &= ~index;
    }
  }

  public BindingFlags Value 
  {
    get
    { 
      return flags;
    } 
    set( BindingFlags value ) 
    {
      this.flags = value;
    }
  }

  public static implicit operator BindingFlags( BindingFlagsIndexer src )
  {
     return src != null ? src.Value : BindingFlags.Default;
  }

  public static implicit operator BindingFlagsIndexer( BindingFlags src )
  {
     return new BindingFlagsIndexer( src );
  }

}

public static class Class1
{
  public static void Example()
  {
    BindingFlagsIndexer myFlags = new BindingFlagsIndexer();

    // Sets the flag(s) passed as the indexer:

    myFlags[BindingFlags.ExactBinding] = true;

    // Indexer can specify multiple flags at once:

    myFlags[BindingFlags.Instance | BindingFlags.Static] = true;

    // Get boolean indicating if specified flag(s) are set:

    bool flatten = myFlags[BindingFlags.FlattenHierarchy];

    // use | to test if multiple flags are set:

    bool isProtected = ! myFlags[BindingFlags.Public | BindingFlags.NonPublic];

  }
}

C++ operations are: & | ^ ~ (for and, or, xor and not bitwise operations). Also of interest are >> and <<, which are bitshift operations.

So, to test for a bit being set in a flag, you would use: if (flags & 8) //tests bit 4 has been set