First off, let me counter some of the nonsense I've already seen: no, the Wikimedia Foundation (the organization that supports Wikipedia and its sister projects) won't lose its tax-exempt status if it runs ads: non-profits are still allowed to make money, as long as they use that money to advance their program. Nor will one get insulted or blocked on Wikipedia for asking this sort of question: in fact, it gets asked so often that it's listed as a "perennial proposal": < http://enwp.org/WP:Perennial_proposals#Advertising >.
That page describes in brief some of the issues. I'll lay them out in an indiscriminate list:
• Wikipedia doesn't immediately need the money. If donations and other sources of revenue can cover Wikipedia without ads, it's better to not run ads than to run ads. To date, donation campaigns and occasional grants have supported all of Wikipedia's needs, including special programs like a Usability Initiative whose user-interface improvements will likely go default in a few months (see also < http://usability.wikimedia.org/ >).
• People hate ads. In fact, plenty of people hate ads so much that, if ads were added, they'd stop editing Wikipedia. This is demonstrably a serious concern because when ads were first *seriously considered*, a significant chunk of the Spanish-language Wikipedia forked to a separate project, the "Enciclopedia Libre". This has widely been seen as having set the Spanish-language edition of Wikipedia back significantly relative to the others. Readers as well don't want ads: people prefer an ad-free experience in general.
• Advertisements give the impression of bias. Modern advertisements, in particular, often are "targeted" such that an article on cheese might be more likely to display advertisements for, say, a Brie or Camembert (that's an unlikely sort of advertising to see online, but I think it's illustrative of the point). If an article on Wile. E. Coyote is advertising ACME products, it's plausible to think that the site in general is supporting ACME, or being paid by ACME to present them favourably, et cetera. Since Wikipedia tries very hard to uphold neutrality, advertisements (which by their nature are non-neutral) are seen as detrimental to the goal.
• Advertisements are ugly, intrusive, annoying, distasteful (especially some of the seedier advertising groups), and all the rest. Site design and feel is ideally not compromised for that.
• Ads can be added if necessary. If Wikipedia were running out of money, if donation drives weren't working, if there were some spectacular failure of a large number of servers, or any other undesirable but unlikely situation, the possibility of ads remains open: a last-ditch plan that would likely spur donations to get rid of them!
There are always a few interesting proposals for ads, and though the community has historically been vehemently opposed to their use, there are a few ideas that I find interesting, including opt-in advertising ("view Wikipedia with ads, and support it without donating directly!") or temporary advertising (to build an endowment that could support Wikipedia's basic needs in the long term).
I'd definitely prefer if there were no ads, and I'd certainly block any ads myself if they were implemented, but Wikipedia's survival naturally takes higher priority than whether or not it runs them.