Certain categories come up time and time again…
Shakespeare
Canadian provinces
US Presidents
Operas
Royal Families
State Capitals
Space Missions
World War II
Nobel Prizes
Blu-Ray 
Although, I’m only partially kidding. The last show before the college tournament featured an HD-DVD vs Blu-Ray and yesterday’s show (the first one after the college tournament) did too.
Of course, Sony owns both Jeopardy and Blu-Ray.
EDIT with serious answers now:
Oscar-winning movies
Presidents
Rivers
Sports, especially baseball and football
potent potables
Last night Potent Potables was renamed Booze-apalooza. I wonder if it’s permanent.
Before I went on I studied most of those - though I knew the presidents pretty well anyhow.
What I should have studied was TV Guide for current shows, since an obscure TV question was the Final Jeopardy one. I also should have studied current music (current 11 years ago) but I lucked out on that one.
They aren’t nearly as highbrow as they used to be.
The Oscars are a frequent category, seems to especially turn up in Final Jeopardy! a lot. I almost invariably miss these questions and then feel stupid when I hear the answer.
The World Almanac (I tried to use this when I was on)
Mountain Ranges
Movie Directors
Ships in Books (they got me on the pronunciation of Pequod)
Canadian-born Game Show Host Deep Dark Secrets
Those Darn Etruscans, anyone?
I do often miss the Oscars ones and then feel stupid.
Also, geography, specifically place names like bays and mountain ranges and such.
Geography
Classical music/opera
U.S. Presidents/politicians
Sports
Those are th categories that stump me the most. Otherwsie I do quite well playing along at home.
Therapists
The Pen Is Mightier…
Colors that end in “urple”.
Months that end in "-ebruary.’
“Febtober?”
Poets & Poetry <shudder>
[ul]
[li]Books of the bible[/li][li]U.S. Presidents[/li][li]U.S. Vice Presidents[/li][li]U.S. state capitals[/li][li]World capitals[/li][li]Names of South American countries[/li][li]Names of African countries[/li][li]Read the wikipedia entry for “opera”[/li][li]If the question has anything to do with Norwegian playwrights, ring in and say “Who is Ibsen?” 
[/li][/ul]
Dupe- sorry
Not having read the thread yet, I apologize for any repetitions:
Recent movies
Grammy Award Winners (my knowledge of pop music is really out of date)
The geography of Eastern Europe and of Africa (these come up a lot)
World leaders (especially of “in the news a lot” countries)
Famous Mothers
Celibacy