Well I have to admit, I'm biased about this topic. Yes there are bands that sound okay without a bass player, but IMO, they would sound better with one. Just about any band I've ever seen live that had no bass player, whether it was Suicide, The Cramps, Black Keys, or even my good friends the Vooduo, when I'm there watching them play, I'm playing along with them, on bass, (in my head) & I hear things that would help tie everything together. @ John B above...Lee Michaels played bass pedals on the Hammond live. Suicide used a bassy tone on their keyboards & played repeating bass patterns much like a bassist would do. No-one mentioned The Doors, they had no permanent bassist, In the studio they used session bassist Harvey Brooks & live Manzarek played Fender Keyboard bass. The Dead Boys used local NY musicians to play bass with them until Jeff made the move from Ohio. One of which was Rudi from The Fuzztones who played live with them at least once at CBGB's.
Also, IMO most of the bands doing the no-bass thing are doing so out of convenience. Take my own former band, The Speedies. They played out for 6 months without a bassist before I came along. I saw them play at Max's and I could feel what they were missing. I walked up to Allen, the drummer & flat out told him, you need a bass player & I'm him. We tried it out the following week, and they never went back to playing without one.