Less than you'd expect, according to John Sides:
That presidential debates can be "game changers" is a belief almost universally held by political pundits and strategists. Political scientists, however, aren’t so sure. Indeed, scholars who have looked most carefully at the data have found that, when it comes to shifting enough votes to decide the outcome of the election, presidential debates have rarely, if ever, mattered.
The small or nonexistent movement in voters’ preferences is evident when comparing the polls before and after each debate or during the debate season as a whole. Political lore often glosses over or even ignores the polling data. Even those who do pay attention to polls often fail to separate real changes from random blips due to sampling error. A more careful study by political scientist James Stimson finds little evidence of game changers in the presidential campaigns between 1960 and 2000. Stimson writes, "There is no case where we can trace a substantial shift to the debates." At best, debates provide a "nudge" in very close elections like 1960,1980, or 2000. An even more comprehensive study, by political scientists Robert Erikson and Christopher Wlezien, which includes every publicly available poll from the presidential elections between 1952 and 2008, comes to a similar conclusion: excluding the 1976 election, which saw Carter’s lead drop steadily throughout the fall, “the best prediction from the debates is the initial verdict before the debates.” In other words, in the average election year, you can accurately predict where the race will stand after the debates by knowing the state of the race before the debates. Erikson and Wlezien conclude that evidence of debate effects is "fragile."
Regardless, Joe Klein expects Romney to do badly at the debates:
It's hard to be effective when you're biting your tongue and swallowing your pride at the same time. Romney has dumbed himself down to fit a Republican Party that has become anachronistic, hateful and foolish. He has never once stood up to the party's extremist base in this campaign–not even when asked whether he would accept a deficit deal with $10 in spending cuts for every $1 in new revenues, not even on immigration and contraception, issues that sent women and Latinos scurrying toward the exits. His has been a shameful, shameless campaign. The public will occasionally turn out an incumbent President, but only when offered a real alternative. Mitt Romney has offered them only a mirage.
The Dish 