It's childish to celebrate the end of what in a lot of people's opinions was the worst Presidency of all time? To a lot of these people, they supported Bush, and then Bush failed to deliver. Many people feel that had Bush not gone so haphazardly into the quagmires of Afghanistan and Iraq, their children or loved ones would still be alive, and yes, I know the mantra of 'Well if you don't want to die, don't join the army' but a lot of these people don't understand what exactly their loved ones died for. To a lot of people, Bush is the devil, as hated by his own people as Saddam was by his people. I know that Saddam committed heinous acts against his people and he hanged for it, but it is not entirely disproportionate; many people do have a level of hate for Bush that strong, and I doubt you were complaining with the way Saddam was treated when his rule came to an end.
Whether Barack will be any better or worse, only time can tell. No one could tell how well Bush was going to do, and definitely could not have foreseen 9/11 and how that affected his government. But for a lot of people, me included, this isn't just a day celebrating a new President, in fact, I'm sure there is a sizeable portion of people celebrating the fact they no longer have to look at Bush as their supreme leader.
Besides, Republicans don't have a right to do anything at the moment. Bush was a useless President and deserved all the crap he got; no one did it just because they felt like it.
At the moment, the international community is in your hand: more or less every country who Bush pissed off in the last 8 years (so, pretty much every sovereign nation on the planet, apart from Israel, of course) loves Obama and is willing to stand beside you, instead of opposing you. Hell, even the Yank-hating UK was jubilant today and ready to love America. The world is quite literally your oyster.