The Windows 7 machine began having a problem where the taskbar would not work any more first thing of a morning. Other jobs ran but you could not start anything. The task manger would not start, so you could not kill anything either. The only way out was to restart the machine from the switch, since the you could not bring up the shutdown/restart dialogue. Cursor still moved and all, so it was not a "freeze".
I had a look at what had recently been installed or updated, and this pointed the finger at iTunes. So I used the service manager to shut down the iTunes' services. iTunes still works though, although there may be trouble when I try to sync. I also stopped the acrobat service. Again, acrobat still works though.
This seemed to resolve the problem. As a bonus, everything seems to start up faster.