Most bands have them, and they help, but I don't think you _need_ a bass player. Most bands have a bass, a drummer, and at least one guitarist, plus a vocalist. I think you can probably take away the bass player or even the drummer and have a decent cover band.
Some will say the bass player is integral to the sound and playing of the band, but plenty of bands have bass players that aren't even audible in the mix. There are plenty of records out there where the bass guitar just doesn't seem audible, and I don't think anyone complains (minus enthusiasts).
If you have two guitarists, a drummer, and a singer, I think you are covered. It really depends on the kind of music you are playing, and what the bass player would do. If the bass player would just be playing the root notes of every chord, it contributes to the low end, but not really to the over all sound; it just adds to the melody that the guitar(s) have already established and that the singer is singing over / harmonizing. That said, some records and bands do have decent bass players that stand out in the mix, but they are a rarity.
Thus, I think, a bass player is desirable, but not necessary, for a rock band.