There is no difference when written on its own (as shown) - in both cases myInt will be incremented by 1.
But there is a difference when you use it in an expression, e.g. something like this:
MyFunction(++myInt);
MyFunction(myInt++);
In the first case, myInt is incremented and the new/incremented value is passed to MyFunction(). In the second case, the old value of myInt is passed to MyFunction() (but myInt is still incremented before the function is called).
Another example is this:
int myInt = 1;
int a = ++myInt;
// myInt is incremented by one and then assigned to a.
// Both myInt and a are now 2.
int b = myInt++;
// myInt is assigned to b and then incremented by one.
// b is now 2, myInt is now 3
BTW: as Don pointed out in a comment the same rules are also valid for decrement operations, and the correct terminology for these operations are:
++i; // pre-increment
i++; // post-increment
--i; // pre-decrement
i--; // post-decrement
As Jon Skeet points out:
  Others have shown where it makes a
  difference, and have commented that as
  a single statement it doesn't make a
  difference.
  
  I'd like to add that it's almost
  always a bad idea to use it where it
  makes a difference. I suspect there
  may be some times where it's more
  readable to have code such as:
Console.WriteLine("Foo: {0}", foo++);
  
  than:
Console.WriteLine("Foo: {0}", foo);
foo++;
  
  ... but they're very rare! The
  latter of these two samples makes the
  ordering crystal clear immediately -
  the former requires a bit of thinking
  (to my poor brain, anyway). Think of
  the readability first.