As you have probably noticed, Windows is monitoring processes and it is tagging the dead or dead-alike ones with "not responding" flag. The framework is giving you the means to track this flag too:
http://msdn.microsoft.com/en-us/library/system.diagnostics.process.responding.aspx[
^]. Still, this is usable only for processes having UI. Services and other background processes can be monitored via the same tools by their activity as you mentioned yourself. But if you made that process you can choose better ways than that to be kept informed about it's status.