Students who are actively applying for and/or obtained external fellowships are of particular interest. It will be easier for you to find a spot in any lab (since you are self-funded), and the fellowship will stand out on your CV. Two of the most prestigious fellowships are the NSF Graduate Research Fellowship and the DOD NDSEG. Others include:
The National Academies website has a very comprehensive list of graduate and postdoc fellowships. Here is another list from their website.

Pathways to Science has a very large searchable/ filterable database of fellowships
The Ford Foundation has Predoctoral, Dissertation, and Postdoctoral fellowships