I don't run it with the browser open. If you click run cleaner multiple times you end up with multiple rundll32.exe processes in the task manager like the OP explained. This only happens if you check Autocomplete Form History.
However I am pretty sure this is not CCleaner's fault, but rather it is the command lines that it uses. Those command line is straight from IE7's InetCpl (RunDll32.exe InetCpl.cpl,ClearMyTracksByProcess 16), which leads me to believe it's got nothing to do with CCleaner.
Oh and by the way, this is with windows XP professional x86 (tried both SP2 and SP3) and IE7 with all latest updates. Not sure if it occurs in Vista, but it should be the same since IE7 works exactly the same in Vista.