find what MPM Apache is using, it will either be using "worker" or "prefork"

apachectl -l
Compiled in modules:
  core.c
  prefork.c
  http_core.c
  mod_so.c


In my case it is "prefork"

vi /etc/httpd/conf/httpd.conf

Find the section that looks like this (by default one will normally exist for prefork and for worker, but in my case I only care about prefork since prefork is what is compiled in):

# prefork MPM
# StartServers: number of server processes to start
# MinSpareServers: minimum number of server processes which are kept spare
# MaxSpareServers: maximum number of server processes which are kept spare
# ServerLimit: maximum value for MaxClients for the lifetime of the server
# MaxClients: maximum number of server processes allowed to start
# MaxRequestsPerChild: maximum number of requests a server process serves
<IfModule prefork.c>
StartServers      8
MinSpareServers   5
MaxSpareServers   20
ServerLimit      2000
MaxClients       5000
MaxRequestsPerChild  4000
</IfModule>

As some have mentioned the MPM prefork/worker sections are VERY important they affect both stability and performance.
In my case I'm the most concerned because I keep getting the MaxClients error message/hung Apache process without error (where Apache thinks it's running but can't connect and yet most of the time nothing in the debug log shows a problem).

Enable Debug:

Speaking of that you might want to enable this for debugging if you're having the issues I've seen (the crash but even with debug it often won't show the true error)

Add this to your config file:  Loglevel debug

Back to the issue, prefork means a new process/server is started for each new connection to the web server.

My new settings:

<IfModule prefork.c>
StartServers      200
MinSpareServers   50
MaxSpareServers   200
ServerLimit      400
MaxClients       1000
MaxRequestsPerChild  0
</IfModule>


 WARNING: MaxClients of 1000 exceeds ServerLimit value of 400 servers,
 lowering MaxClients to 400.  To increase, please see the ServerLimit
 directive.

Change ServerLimit to "4000" and restart