Call of Duty is probably the best of the "simple" shooters I have played. By "simple" I just mean in contrast to tactical, one-shot-kill type action games. Call of Duty isn't a realistic shooter in terms of gameplay, but it is easily the most movie-like action game around. If you can imagine what it would be like to be in a movie such as Saving Private Ryan or Enemy at the Gates, this game is it. The sound effects are fantastic, helping you feel the chaos that is war going on around you. You really feel like you are part of a larger battle while you are working with your company.
Many missions present you with objectives that seem like crazy suicide, such as running across an open field with little to no cover; definately movie-like (and somehow, you'll actually make it). The weapons are portrayed accurately enough to feel like you are really in the World War II era (more games need to encorporate the use of iron sights).
The A.I. in Cal of Duty is certainly competant, on both sides. You never command your squad, so their advances are scripted to your movements, which is done well for the most part. However, there were frustrating moments when I wanted to have my teammates hold back while I went ahead and picked off a gunner myself, and I couldn't tell them to. I suppose that's accurate to how war goes when you don't call all the shots.
Call of Duty can be summed up in one word: Fun. Although gripping, exciting, intense, cinematic, and awesome are all good choices as well.