Check out Doom Resurrection. It's kind of short, but great fun while it lasts. Time Crisis is supposed to be pretty fun as well. I haven't tried it myself, but you might want to look into it after you check out Doom.
Actually, Doom Resurrection was extended with new levels and it's now quite a bit longer than it used to be. I would also take a look at Galactic Gunner -- that one is short, but it comes the closest to recreating that arcade experience.
