Personally, I think Blair would have been absolutely fine had it not been for Iraq (granted, some people have other grievances as detailed above) - people were generally displeased that he lied to parliament in order to go to war and outright ignored any advice he was given regarding going to war in Iraq.
He could have even survived that (though he still would have lost a lot of support) had he gone about it honestly.
Blair's also introduced reforms which although they have gained him a lot of support, they're also rather divisive - for example, devolution. Personally? I'm for devolution, but there are plenty of people who aren't that Blair has annoyed.
To be honest, Blair hasn't actually done a bad job (note that I said not bad, I didn't say good) - everyone always says crime is through the roof and it's the end of the world, but it isn't really any different than it has been.
The NHS, although it does have several problems is second to none in an emergency (my grandfather's life has been saved multiple times by the NHS), and although it faces problems, they're not irreversible (as demonstrated by Gerry Robinson - without costing a penny).
Immigration? That's another one that actually tends to get rather hyped up, but a glance at a demographic map will allay the fears of even the most far-right bigot.
Overall, Blair's hardly been a wonder, but (as with pretty much any government), the problems under his premiership generally aren't actually that much worse than they have been in the past. His big downfall was over Iraq and the recent peerages scandal.