I agree with most of what's already been written.
Personally, the reason I started doing wet-lab work is to gain credibility. I'm currently finishing up a Ph.D. in the comp/sys bio. When I started, I had prior experience working on computational aspects of biological problems, but had no wet experience to speak of.
I had no intentions of doing wet-lab work either, but I quickly realized that even at the most prestigious institutions, the "computation-only" people are somewhat relegated. Of course, there are good scientists everywhere who realize the value in what we do, but the majority of people in the life sciences see our work as somewhat of a sideshow, and some go to the extent of resentment because, well, computational biologists don't have to take time-points at 3 a.m., they can work just as easily from home when they need to, they sit relatively comfortably at a desk rather and don't run around with cancer-causing agents, etc etc.
Also, most computational work is at the analysis end, and hence computational biologists are usually the ones who check whether the experiment worked, the hypothesis is correct, etc. Being in this position is exciting because you get to see the actual results and come up with conclusions, but the flip-side is that you have to be the one to tell the army of pipettors that they're wrong...
Once you start doing wet-lab work, and get good at it, you'll most likely notice a world of difference in how your colleagues treat your ideas! So learning wet-lab skills is very useful for that aspect alone!
As far as what skills you should pick up, it's hard to say. I have found that really the ONLY way to pick up a wet-lab technique or a new programming language for that matter, is to do a small project that requires the skill. Also, the best part is that wet-lab work is EASY--ignore what your colleagues tell you. It's hard work, sure, but if you can cook something simple according to a recipe, then you can be good at wet-lab work...it's actually easier because the recipes are much more precise.
Last, from personal experience, I can tell you that wet-lab work is grueling, but it can be quite satisfying. Say, you found a faint hint of a very interesting effect in a huge mess of data that can be a big, big deal -- don't YOU want to be the one to perform the follow-up experiment and test it for real?