Nicki Minaj videos are available at the Youtube channel NickiMinajAtVevo. The account also features audio for some Nicki Minaj songs that don't have music videos.
The Nicki Minaj Vevo account on Youtube also features related channels such as MeekMillTV and RihannaVevo, as well as playlists such as "Vevo HQ Urban Mix," which include Minaj's music videos along with music from similar artists. The "video" section of the Youtube page allows users to sort by either newest to oldest video, or most to least popular video. Another way to watch Nicki Minaj videos is to go directly to Vevo.com, but the page also includes recommended artists, not just Minaj's videos.