This is an interesting question because there are pros and cons to university involvement. Obviously, the funding that a university can provide or the support necessary to get funding is a major pro for the university. On the other hand, being involved with the university could mean a lot of top-down intervention that isn't necessarily attractive. Case in point, a friend has designed a lovely Omeka site of materials from the collections at Emory - materials for which Emory owns the copyright or there's enough latitude with the copyright laws to not worry - and the library's lawyer refuses to let the site go live over copyright issue. This reminds me of @elotroalex's suggestion about #GuerillaDH, which similarly has the advantage of going it on your own but the downside of little-to-no institutional support.