Re: Bass Player-less band?
It seems that few bands can really deliver the goods without a bass player. Some successful bands sans bass have already been suggested but they are rare. (I would like to add one of my favorites: the Cramps! RIP Erik "Lux Interior").
There are other genres of music that do not always have bass players (e.g. Sufi, some surf, some latin, etc). So whether or not you can be successful also depends upon the style of music you are playing.