Is it possible to provide feedback on a colleague's code, without him/her getting offended? I haven't figured this out yet..

I'm interested to know as well

Try this:

"Have you considered (...)? We can write down the pros and cons of the different approaches and decide what is best."

This way you give him/her the opportunity to discover more solutions to a problem without pushing a certain direction.
You also may be wrong, he/she may give you a valid reason why it's done the current way.

And always, ALWAYS, provide your review with information from books or valid websites.

@BikerMouse, you have good experiences with that approach?

What also helps is to stay open for discussion yourself. If someone reviews your code, consider their answers. This makes it more acceptable for others to listen to you as well.

@anroven you will always have stubborn asses. But my colleagues and I work this way and we learn a lot.

Yeah it is possible. We do code reviews all the time and add comments where we express our personal opinions or tasks if code really needs some work. It's not a matter of offending each other but a matter of improving quality and it'll make you a better programmer as well.

I always try and focus on the code and suggest ways it could be improved. If someone has asked for my help then I expect them to be receptive to feedback.

It works both ways though, you have to be open criticism as well.

I think it's all about the approach. If you start off thinking that you're absolutely right and not open to dialog, I'd probably be shitty about it too.

Give people an in. Avoid certain language. "You shouldn't...", "Why would you...", etc will take more effort from the person you're criticizing to not punch you in the face.

If you listen to them, they're likely to listen to you too. There is, however, some people looking to be offended no matter what you do.

Yes. Set up an official code review process, and apply it to everyone.