Do Watch:

The West Wing
Brilliant, delightful, optimistic melodrama with very high highs ("Two Cathedrals") and lows ("The Stackhouse Filibuster") that are still better than most shows' best episodes. I actually watched this once while loopy on pain meds after a wisdom teeth extraction and it was like ten times the rollercoaster of emotions it normally is. It was honestly one of the greatest viewing experiences of my entire life.

Buffy the Vampire Slayer
I can't think of a more enjoyable form of escapism than Buffy, and though its final season is looked down upon, the series was wrapped up with a satisfying conclusion that wouldn't leave a person disappointed on their death bed.

Freaks & Geeks
There weren't a lot of episodes, but you're not going to find more quality in such a scant quantity than Freaks & Geeks. Besides, Sam Weird needs you, and you can't leave this world not knowing that punkers don't call themselves punkers. You'd get your ass kicked in the after life.

The Office (UK)
Another short one at only 14 episodes, the original Office series wrapped up perfectly and is one of best things ever created for the television medium. If you're looking for a sitcom to watch before you go, this is the one to make your mission.

Lost
If your prognosis leaves you alive until next May's guaranteed-to-be-mind-blowing series conclusion, this crazy ride of a show will get your pulse (and mind) racing one last time.

Don't Watch:

Sex and the City
Besides its constant vapidity, everything that was mindlessly enjoyable about this series vanished in its later seasons. Yes, it is difficult to prevent people on any long-running show from becoming parodies of themselves, but this is the shining textbook example of how not to write enduring characters.

Battlestar Galactica
A beautifully genius show... until the end, which wasn't just disappointing, it was absurd. And I don't know if anyone's ever mentioned this before, but it's also slightly bleak. You might want to watch something happier in your state.

Heroes
If you don't have a lot of time left, don't let the decent first season hook you into suffering the following two. Even you have too much to live for.

The Sopranos
Critically acclaimed, well-acted, thrilling (when it wasn't boring, let's be honest) and groundbreaking television, its open-to-interpretation letdown of an ending will just frustrate you. It's just not worth it if you can only see one more series.

Grey's Anatomy
Another example of a show that started out well and just went from good to bad to worse to nearly unwatchable over the course of five seasons. It could very well come back with a vengeance next month and ultimately wrap up well whenever it ultimately ends... but let's just say we wouldn't prescribe it on DVD to the person without time to spare.