Wow, y'all who've never seen stem shifters are making me feel awfully old...
I've found stem shifters to be adequate, but I prefer downtube or bar end shifters on older bikes. Stem shifters typically were on lower-quality/priced bikes. I found them kindof unstable when shifting.
For you young'uns, shifters integrated into the brake levers are a pretty new development...I had never tried them until I bought my Luna in 2005. But that might be because the bike that my Luna replaced was a 1983 Vitus with downtube shifters. Classic!
Oakleaf - bar end shifters are fantastic (to me). Very stable. You can see what gear combo you are in by looking at the shifter position instead of having to (dangerously) look down at the chain rings/cassette. Easier to fix than integrated shifters, too, if you are on the road and in a remote place. Easier to adjust. Easier to use than downtube shifters because you don't have to move your hand as far. The only drawback for me is that they do extend the length of the bars, and I'm kindof a klutz and so I'm always bumping my leg into the shifters, which result in some interesting bruise patterns (I bruise easily).