That depends entirely on the model in question.
I have had two myself, a simple 7" Vidikron video-grade machine which was almost completely silent, having only a single and fairly slow fan.
My present one, a Sony 1292, a 9" monster which is supposedly the most noisy CRT projector ever made, with 14 fans, is indeed VERY loud - loud enough to drone out the dialog in the most quiet passages of a movie.
Some models are varying the fan speeds, so they in effect have variable noise levels. I have heard a Barco 1209 which is substantially more quiet than my Sony, but according to the owner, the fan speedup that takes place when it's been running a few hours, is still enough to make the noise annoying.
If you look around in this forum, you will find many posts about hushboxes and fan modifications, so lowering the noise level is a desire for the owners of many different models. The general opinion regarding noise if you compare CRT to digital projectors though, seems to be that the CRTs often have a less irritating noise spectrum, since they typically use larger and slower rotating fans than the smaller digitals.