1st and 2nd Doctors: many of the episodes have been lost or otherwise wiped, so you won't have much luck with them.
3rd Doctor: Planet of the Spiders. This is the one where he regenerates into Tom Baker (there will probably be a lot of regeneration episodes here; they tend to be good).
4th Doctor: Genesis of the Daleks is one of the best Doctor Who stories ever. Definitely worth a look. Also probably an idea to check out Logopolis, which is his regeneration episode. His actual death is a bit rubbish, but it's still worth seeing the end of Tom Baker's seven-year run.
5th Doctor: The Caves of Androzani. This, along with Genesis of the Daleks, is up on my list of best Who stories ever. Again, it's Peter Davison's regeneration, and he's one of the depressingly few Doctors to actually get a heroic death.
6th Doctor: not a fan, personally.
7th Doctor: Remembrance of the Daleks, for their last appearance before the revamped series. Also Survival, which, while a bit weird, was the last story before the show was cancelled.
8th Doctor: only had the TV movie. It's ok.
9th Doctor: Dalek and The Empty Child are probably the best of his run, and it's not a coincidence that they're both by Steven Moffat. The finale, The Parting of the Ways, is spectacular.
10th Doctor: Blink. If nothing else, you need to see Blink. It's absolutely sublime, and probably the best episode of the revamped series to date. Other than that, Human Nature is very good, as is Last of the Time Lords, the finale of Tennant's second season.