I'm a big fan of the West Wing. The first four season were very very good. It loses the thread toward the end of the fourth season, and doesn't really recover until the final story arc in season 7, but on the whole very satisfying.
In my mind, the greatest moments will be the cliffhanger ending of season 1 (Thank God I watched it from the DVD box and didn't have to wait for the next season) and, probably the best in my opinion, the scene in Two Cathedrals where the president curses at God, often in Latin. That is what they call drama.
If you're considering it, I'd recommend starting from the beginning. It doesn't have as many growing pains as most shows, so what you see in the first two or three episodes is pretty much the style of the show. A lot of walking and talking, very snappy dialogue, and real world problems bandied about in a 60 minute snippet of entertainment.