Halo>>>Doom>>>>>>>>Everything else
Halo is just the best by a mile. Excellent gunplay, never had a bad entry (certainly some better than others), and is largely responsible for the rise in the popularity of the genre in the early 2000s.
Doom was the original awesome FPS, and established the genre as one of the big ones. The fact that they've managed to completely modernize the series, while maintaining the Doom feel is awesome.
Beyond that, there are many good shooters. But, I don't think any of them deserve to be in the conversation with these two, with the possible exception of COD (it's just huge). Maybe Destiny as well, if one considers that a FPS.