What's the services/running processes manager in Mac OS X? I installed MySQL but I am unable to see if it is running or has stopped. How do I see what are the currently running services corresponding to the "Services" interface in Windows?
For most of the "services" (called Daemons or Agents) you can check:

In terminal: sudo launchctl list

For example only MySQL you can filter the output of the command above, like sudo launchctl list | grep -i mysql. Note -i is to make the filter case insensitive.

These can be controlled with a GUI named Lingon.

There are some other "services", that will install themselves in:

/Library/StartupItems


For those, there is a command like 
ps -ef |grep /Library/StartupItems to view whether it is loaded and running. But there isn't a generic mechanism to stop, start or restart.

In which category your MySQL installation falls is impossible to say, as your question is lacking details on what exactly you have installed, what its source is, how it was installed, etc..