Here are some answers in bold.
What kind of games do you enjoy?
Games with a theme, games with auctions and bidding as a mechanic. Games with different choices and types of play but each choice is a win
Abstract type games with simple rules but strategic and or tactical depth (like Chess, Go, etc...)?
Theme heavy games that may be a lot of fun, but also somewhat fiddly as well?
Beowulf, Shadows Over Camelot
Streamlined euro style games with some strategic depth?
Beowulf, Adel Verflechtet, Stone Age
Really deep euro style games that may be a bit of a brain burner?
I don't really know what you mean between this question and the last one.
Cooperative games?
Shadows Over Camelot (and it's hard enough to win without a traitor playing so it's kinda more fun with no traitor), Fortress America
Confrontational games?
Diplomacy of course! 
Cosmic Encounter
Card games?
Apples to Apples
War games?
Miniature games?
Space Hulk
What kind of play time would you want for your games?
1-2 hours. Occasionally a 3-4 hr game is fun but I'd better like the people I play with. 1/2 hour games are fun too.
If interested in games with theme, what are some of your favorite type of themes?
Fantasy, Horror, having a country or era as a theme
New categories:
Storytelling/RPG type game:
Tales of the Arabian Nights
Abstract/Art: Dixit