When my computer is running, there are between 37 and 40 processes going all the time. Is that many normal, or is there a way to clean it up to only the essentials?

   I have 29 processes when six programs are running.

It all depends on what programs you are running. I have 43 processes currently running. None of them are currently using CPU time though.
I use Norton System Works and Symantec loads a lot of processes with it.
Most programs you install will also try to add a process to do periodic updates or provide links to their Internet site.