I've had problems hitting the maximum number of processes on my Verio
vps2, which is 75. Total, for mysql, sendmail, cron jobs, etc. It
seems like Apache needs to be limited to at most 30 processes. This is
at odds with all the default and suggested parameters, such as maximum
clients being 150-512. Setting something like that to 30 seems overly
restrictive. Unfortunately when I hit a total of 76 processes the
server freezes and stays frozen until I can get somebody at Verio to
reboot. (And they won't even take a call from me, I have to call the
reseller I use, who in turn has to call them.) I'm not running
anything unusual or particularly busy. If apache reaches 35+ processes
on this Verio virtual private server I get dangerously close to the
fatal limit.

http://httpd.apache.org/docs/1.3/mod/core.html#maxclients

Set maxclients to a lower number.  It defaults to 256.  

Dan

http://httpd.apache.org/docs/2.2/mod/mpm_common.html#threadlimit
and
http://httpd.apache.org/docs/2.2/mod/mpm_common.html#serverlimit

The ThreadLimit directive may be more what you're looking for with
Verio's limitation requirement.  This, in conjunction with
ServerLimit, and MaxClients, will do the job.