Something like this might work:
[^/]*$
It matches all characters to the end of the line that are not "/"..
If you want to match paths that use the "\" path separator you would change the regex to:
[^\]*$
But do make sure to escape the "\" character if your programming language or environment requires it. For instance you might have to write something like this:
[^\\]*$
EDIT
I removed the leading "/" and trailing "/" as they may be confusing since they are not really part of the regEx but they are very common of representing a regular expression.
And of course, depending on the features that the regEx engine supports you may be able to use look-ahead/look-behind and capturing to craft a better regEx.