The popularity of co-ops varies by jurisdiction. There are numerous co-ops in DC (and NYC of course) and very few in Virginia. In my experience, a co-op "lives" like a condo but has different paperwork and financing requirements. In a co-op you are buying essentially shares in a corporation, or personal property--a lease that entitles you to the use of a particular unit. There aren't particularly advantages or disadvantages in my opinion, except in your personal viewpoint--just differences.
-In a condo, if you can buy the unit, you can live there and **potentially** rent it out per condo rules. In a co-op you will have some form of interview (could be in person with one or more board members, or could be a paper questionnaire (such as River Place in Rosslyn). Some co-op boards may screen you out, for example, if they perceive that you intend to rent out the unit rather than live there.
-Financing a condo is like financing a house, you get whatever mortgage you can get, and you can get pre-approval so you know what works for you before you fall in love with a property. Financing a co-op is possible only through a small group (could be one, could be a handful) of lenders with more restrictive financing rules than for a condo. For example, you often need at least 20% down payment. Your rates may differ from the prevailing rates for "regular" mortgages--remember, the range of available lenders is smaller and hence less competition and possibly more risk for the lender. Co-ops often have an "approved" list of lenders they allow.Hence when you are house hunting, you may not have a clear picture of whether you can afford a particular property until you pick one out, rather than pre-qualifying with confidence about what you can afford.
-Monthly fees may be higher in a co-op relative to a similar condo. In some co-ops the monthly fee includes a portion of the underlying mortgage that bought the entire building a few years ago--but this portion would be tax deductible to the extent that any mortage is.
-Before you start house hunting, go ahead and get a solid lender pre-approval so at least you know what is possible. If you fall in love with a co-op, you at least have a head start with your documentation and thoughts.