It seemed like a good idea at the time. To most Americans anyway. It was March, 2003, and 64% of Americans supported the idea of invading the state of Iraq. The case made to justify the invasion to the community of nations assembled at the UN was almost entirely Iraqi failed compliance with UN weapons inspections, but as far as the American public was concerned, Iraq "probably" had something to do with September 11th 2001. Anyway, it seemed like a good idea at the time.
It, of course, had nothing to do with September 11th, and everything.
Saddam Hussein's part in it actually makes the most sense. He was a psychotic dictator, but he fell victim to the achilles heel of all psychotic dictators: you must stay in power at all costs. No state is a fairy-tale kingdom where no one questions the rule of the leader, and when you're a psychotic dictator, more than ever, you've got to keep people thinking you're totally on top of things. As such, and its come out since that this was his intentional strategy, Saddam purposely kept everyone thinking he had weapons of mass destruction and was in a powerful enough position to give the UN the bird. If he didn't, he may have been ousted by his own generals, and when "reign of terror" is your form of government you'll do anything not to be the ousted guy. All the civilized world's "shock and awe" is preferable to being the ousted guy.
As for Bush's motivation, things are a little less clear. I never for a second bought that he actually thought Iraq posed a threat to us. I also have never bought the "we're doing it for oil!" explanation -- it's not like we ever stood to get oil for free from the place. The most cynical explanation I'll entertain is that it's a strategic location for us to have a military presense. In particular it means we surround Iran, who DOES scare us.
A second explanation I actually give some weight to is pure psychological issues. Father issues even. Bush's father didn't finish the job, and in fact Saddam tried to have Bush Sr assassinated. Now Bush Jr had the opportunity and was out for blood.
But this is a democracy, and really, it comes down to The People. And THE PEOPLE wanted blood. It was becoming alarmingly apparent that we weren't about to find which hole Osama was hiding in, and The People wanted blood. No one even had to say there was a connection between 9/11 and Iraq for Joe redneck and 64% of the rest of Americans to be certain of it. Frankly, Bush probably would have lost the election in 2004 if hadn't kept The People satisfied he was kicking the shit out of someone to satisfy their need for blood. It seemed like a good idea at the time.
Six years later, it doesn't seem like such a good idea anymore. Turns out "WE WERE TRICKED" into believing Saddam's socialist secular regime had teamed up with radical arch-conservatives who wanted to blow us up for being too secular. Turns out the Weapons of Mass Destruction everyone was so eager to believe were "probably" there in fact probably weren't and furthermore with the brilliance of hindsight we're now certain we shouldn't have ever thought they might be there. It now seems like a terrible idea.
And in fact, never mind that most Americans supported the war, never mind that the Congress authorized it. Never mind that Hillary Clinton was for it before she was against it -- she voted to authorize it when it was popular in 2003, now its clearly all someone else's fault and in 2008 she had better be seen kicking the shit out of someone to satisfy the need for blood. And now, that someone is George W Bush.
...at least life as an ousted leader is better in the United States, and he didn't have to resort to playing chicken with the UN to stay in power (instead he played rooster to the UN's hen just for fun).