How can I apply a function to every row/column of a matrix in MATLAB?

Many built-in operations like sum and prod are already able to operate across rows or columns, so you may be able to refactor the function you are applying to take advantage of this.

If that's not a viable option, one way to do it is to collect the rows or columns into cells using mat2cell or num2cell, then use cellfun to operate on the resulting cell array.

As an example, let's say you want to sum the columns of a matrix M. You can do this simply using sum:

M = magic(10);           %# A 10-by-10 matrix
columnSums = sum(M, 1);  %# A 1-by-10 vector of sums for each column

And here is how you would do this using the more complicated num2cell/cellfun option:

M = magic(10);                  %# A 10-by-10 matrix
C = num2cell(M, 1);             %# Collect the columns into cells
columnSums = cellfun(@sum, C);  %# A 1-by-10 vector of sums for each cell

Adding to the evolving nature of the answer to this question, starting with r2016b, MATLAB will implicitly expand singleton dimensions, removing the need for bsxfun in many cases.

From the r2016b release notes:

Implicit Expansion: Apply element-wise operations and functions to arrays with automatic expansion of dimensions of length 1

Implicit expansion is a generalization of scalar expansion. With scalar expansion, a scalar expands to be the same size as another array to facilitate element-wise operations. With implicit expansion, the element-wise operators and functions listed here can implicitly expand their inputs to be the same size, as long as the arrays have compatible sizes. Two arrays have compatible sizes if, for every dimension, the dimension sizes of the inputs are either the same or one of them is 1. See Compatible Array Sizes for Basic Operations and Array vs. Matrix Operations for more information.

Element-wise arithmetic operators — +, -, .*, .^, ./, .\

Relational operators — <, <=, >, >=, ==, ~=

Logical operators — &, |, xor

Bit-wise functions — bitand, bitor, bitxor

Elementary math functions — max, min, mod, rem, hypot, atan2, atan2d

For example, you can calculate the mean of each column in a matrix A, and then subtract the vector of mean values from each column with A - mean(A).

Previously, this functionality was available via the bsxfun function. It is now recommended that you replace most uses of bsxfun with direct calls to the functions and operators that support implicit expansion. Compared to using bsxfun, implicit expansion offers faster speed, better memory usage, and improved readability of code.

I like splitapply, which allows a function to be applied to the columns of A using splitapply(fun,A,1:size(A,2)).

For example

A = magic(5);
B = splitapply(@(x) x+1, A, 1:size(A,2));
C = splitapply(@std,  A, 1:size(A,2));

To apply the function to the rows, you could use splitapply(fun, A', 1:size(A,1))';

(My source for this solution is here.)