I used to use TeraCopy when that was the only thing available that could do basic file integrity checks. Now I use FastCopy, which is faster, free, open source (BSD instead of GPL!), and has many more features. The best part is that it's available in the PortableApps suite, so you always have it with you, and you never have to worry about checking for new versions (it's automatic).
[Edited by blackboard, May 29]