This one had bothered me for a quite some time...
I have a development machine with MOSS 2007 and BizTalk installed. Even though I was dealing with only one server, I tried to follow best practices as much as I could when setting up the box. So I had different accounts as service accounts for a bunch of application pools that were responsible for central admin, ssp, mysites and so on. I ended up with about 15 application pools.
At this point, I noticed that among the central administraction, share service administration, mySite and my main site collection, I could only access 2 of them successfully. As soon as I hit the third one, it always returned "Service Unavailable". The event log said that the application pool was stopped due to repeated failures.
Eventually I cam across this article: http://support.microsoft.com/kb/831135 about large number of application pools on IIS 6 and UseSharedWPDesktop registry setting. Even though the article says that you need to use this setting when the number of application pool with unique identities is over 60 and I have only 15 in my case, I went ahead and added the setting. After that and resetting IIS, all problems are gone.
I guess it doesn't take 60 application pools to exhaust the resources, after all.