A common complaint about Open Access Journals is the difficulty in determining whether they are reputable or not. The only way to truly know if a journal is reputable is to do some investigation into the particular journals you are interested in.
There are some resources that can help you make informed decisions:
Jeffrey Beall has become synonymous with identifying "potential, possible, or probable" predatory OA publishers. To gain a brief background on the Beall blacklists, opportunities for whitelists, and librarians' roles in promoting OA publications, you can read this article from College & Research Libraries.
Perhaps the most useful item from Beall's site is the publication of his evaluation standards.
Another way to determine the quality of an OA Journal is whether it is indexed in a reputable database or by a major publisher. Since they have their own inclusion criteria for journals, you know the journals have passed at least some level of scrutiny.