Short answer: Not much.
Prior to this week, a lot of pundits wondered why Obama was holding his fire while McCain roughed him up on a near-daily basis. The argument against firing back was the analogy to the Democratic primaries: Around this time last year, we all wondered why Obama wasn't knee-capping Hillary. But Obama more or less stuck to his no knee-capping policy (at least up to Iowa), and it worked out pretty well for him. No one could be sure it wouldn't work the same way in the general.
I don't think so, for two reasons:
1.) In a Democratic primary, it's incredibly tricky to go negative on a woman who's beloved by half the party, well-respected by at least another quarter-to-a-third of it (or at least she was at the outset), and who evokes unpredictable emotional responses across the board. Much easier to go negative on an old white guy. (Though probably slightly less easy against someone like McCain, who's historically appealed to independents.)
2.) Obama had two major assets in the primaries. The first was his early opposition to the war. The second was the perception that he practiced a new kind of politics. Both allowed him to favorably distinguish himself from Hillary. Outside those two things, there weren't many differences between them--no major policy disagreements, for example--and the few that existed (experience, say) tended to favor Hillary.
If Obama had gone negative, he would have ceded one of those two key assets (new politics). Worse, blurring distinctions tends to favor the frontrunner, which Hillary was until Iowa.
In the general election, Obama has a different set of assets. The first is that his policies are more popular than McCain's. The second is that voters prefer Democrats to Republicans by a wide margin this year. The third is that George W. Bush is radioactive among everyone outside a small group of Republican partisans. The fourth is that voters see Obama as a credible change agent in a year when 80 percent of them think we're on the wrong track. The fifth is that he represents a vision of the country as unified.
Unlike the primaries, going negative actually enhances most of his assets in the general--it draws attention to McCain's unpopular policies, it remind voters that McCain is a standard-issue Republican, it links McCain to Bush. I think the effect on the fourth asset is netural--voters will see Obama as a symbol of change regardless of what he does, since he's not only a Democrat but young-ish and black and has a foreign-sounding name. (Obama's problem isn't that voters doubt he'll bring change; it's that they worry he'll bring too much change.) The only risk is the unity theme, which I think Obama and his campaign are deft enough to finesse. (When going negative, you basically frame the race as George Bush and John McCain versus the rest of us.) In any case, this particular asset, while central to Obama's political identity, is probably less important than the previous four.
Almost by definition, the primaries were about demonstrating why Obama should be the Democratic standard-bearer, which made it necessary to focus on the Obama brand and made anything that tarnished it (like going negative) pretty risky. But in this year's general election, any minimially acceptable Democrat will do. And so any damage to Obama's particular appeal is less important than it might otherwise be.
UPDATE: Click here for Mike's take on the question.