Do you remember why we supported Iraq in the first place? Because Iran was (and is) a huge threat to the region. It's a militarily powerful nation run by (and composed of) the most hard core fundamentlist Islamics. Of course, let's ignore that we put them there. We helped stage a coup to get rid of the original government (mainly because they'd nationalized their oil fields). The new ruler was something of a nasty dictator (but did fix the oil field problem) whose populace hated him and his secret police. Which meant there was another coup, this time by Khomeni. And the Shi'ites.
We were worried that Iran would take over everything. So we funded and trained Iraq to stop them. After Iraq and Iran got into it, Oliver North got the bright idea to sell weapons to Iran (backstabbing Hussein in the process, eh?) in exchange for terrorists (and we all know what happened to that money). Then Iran started winning, due in no small part to the weapons we started selling them. So we gave Hussein chemical weapons and delivery systems, which he started using. Once again, stalemate.
Then Saddam, tired of basically paying to defend the entire Middle East against Iran (of course, he didn't mention his own desire for power), asked Kuwait to forgive his debt, and he'd drop the whole slant-drilling topic as well (assuming Kuwait didn't start doing it again). Kuwait said no. Hussein spoke to the US Ambassador, and believed the US would stay out of it. (No transcript of this session, save the Iraqi one, is available. However, the US Ambassador did say something to the effect of "No one thought he'd take all of Kuwait" somewhat later, and the State Department has refused to clarify which portions of the transcript are inaccurate).
He invaded, thus Desert Storm. We left him in power for two reasons. First, it'd be somewhat costly to dig him out of Baghdad. But mainly because we still needed a foil against Iran.
So, what happens if we take out Saddam? Well, we can't institute a real democracy. The majority of Iraq is Shi'ite. Just like Iran. And it's not like we've stopped worrying about Iran....And then, of course, invading Iraq would tick off most of the terrorist groups (many of whom formed because the West got involved in what they considered a private matter, to be dealt with by Muslims), and alienate the general populace of the Middle East. After all, nasty as Saddam is, they're going to consider us wandering in, starting a war, and taking over a country (especially as they will believe we did it solely for cheap oil) as something to be very angry about.
So, in one fell swoop, ridding ourselves of Saddam will lose us any public support we have in the Middle East, swell the ranks of terrorists, make Iran an even bigger problem than it was.
As for gassing his own people: So have we. Or weren't you watching the news?