Should a band always have a bass guitar?

I'd say it's not absolutely necesary to have a bass player in the band.

However, you should know that the overall feel, power and presence

of your band's sound lays heavily on the firm, solid base that the bass

player creates. Not only does he(she) provide the entire support for the

other instruments (along with the drums), they also make the sound a lot

fuller and lively. Without the bass, the band is most likely to sound empty.

But still, if you can't find a bass player there are other instruments like a

piano or syntheziser that can fill in for the bass parts. The important thing is

to have a solid base on which the other instruments can rest. There is no one right sound for any band. And as long as there is an instrument that has a tonal range extending into the bass frequencies, you also will not lose the "bottom" in the music. Examples of bass-less bands include Sleater-Kinney (where rhythm guitarist Corin Tucker's guitar tone and style almost serve as a bass), The White Stripes, and Led Zeppelin in certain live situations when bassist John Paul Jones would play keyboards, and employ sounds that have a solid bottom. A band with a piano often doesn't need bass at all, given the piano's powerful low-end sound, percussive clarity, and full sonic spectrum. Conversely, you have a band like Motorhead, which has a bass player (Lemmy Kilmister) who makes his bass tone much higher ("buzz bass"), sounding more like a rhythm guitar than a bass.