The best website for reading about these questions is probably 911Truth.org, and one good place to start is their "Top 40" page. Some are strong questions, some are not. Here are a few of the stronger ones:
Not on this list is, for me, one of the strongest arguments: The "Visa Express" program:
The Visa Express program [introduced in May 2001] was a U.S. State Department program that allowed residents of Saudi Arabia to enter the U.S. without proving their identities. It became controversial when some of the 9/11 hijackers used this program to gain entry into the country, and the program was eventually shut down... The U.S. had recently concluded that Saudi Arabia was one of four top nationalities of al-Qaeda members... A senior State Department official described the program as "an open-door policy for terrorists." No other country had this system to facilitate easy entry into the country.
Ummmmm.... WTF? If this was, say, England we were talking about, it would still be an issue, but somewhat understandable. But we're talking about Saudi F-----g Arabia here! Whose brilliant idea was this? HELLO? Anyway, convenient timing, no?
There's also stuff about the Florida aviation school where the terrorists trained that had all sorts of shady dealings, including drugs and politics. But it's not as solid as some of the other stuff, and it would be downright irresponsible of me to mention that the school also had strong connections to Jeb Bush and Katherine Harris, both very prominent in getting Florida for George W Bush in 2000. So I won't do that...
As a counterpoint, Popular Mechanics has an article debunking several conspiratorial claims, but they don't address most of the questions being raised, although they do address quite a bit. They also take a snooty attitude to what are quite legitimate questions - as if questioning the official story is offensive somehow.
I'm personally taking a cautious approach: I'd like to think that there is no conspiracy, and that the official explanation is correct, but without answers to some of these questions (particularly Visa Express), I can't fully believe it.
UPDATE: I just noticed that the Popular Mechanics article redirects to hess.com! Who has, as I've mentioned before, Thomas Kean on their board. Jeez...