The main advantage is more bang for your buck, as you can get a slightly bigger or nicer apartment, as compared to a same priced condo
Also, you get to pick your neighbors, if you are on the co-op board....

Maureen, Joseph makes good points, coops are not for everyone. However, many condos in Manhattan are acting like coops these days. Ever since 9/11 condos have been tightening their rules. Many have the same board packages as coops and many are now interviewing buyers. Most buildings in Manhattan are still coops. Most condos are new buildings. Pre war condos are rare but do exist. The original buyers bought directly from the sponsor. Even in a coop when you buy from a sponsor (unsold shares) there is no board approval. As the buildings mature and the owners take over the board from the sponsor (developer) they want to impose more rules. I live in a condop which most people think is a coop with condo rules. Not quite but another topic. Coops are fact of life in Manhattan especially if you want a pre war apartment. Unfortunately condos are becoming more like coops rather than the other way around. Today's front page of The NY Times real estate section is titled Condos Tighten The Rules

The qualities which make a co-op desireable (mostly owned occupied, somewhat lower transfer fees) must be weighed against the disadvantages to particular owners. If you forsee the need to sublet, a co-op is not an advantage because many co-ops forbid sublets or make them very difficult . In some buildings the requirements to purchase can be extremely strict (no financing above 75% or worse) so when it comes time for you to sell, you have to worry about finding a buyer who will be approved by the Board (condos have no ability to reject your buyer). Also, some co-ops have "flip taxes" which impose a tax on the owner's profit. That's not an advantage either.

Coop ownership offers more of a "quality of life" community environment. A large portion of the monthly maintenance fee is tax deductible. Closing costs for coops are significantly lower than for a condo. Coops are not subject to NY State mortgage tax because they are considered personal property rather than real property.