To answer the question frankly: It depends entirely on the OS and app design, but this question may indicate a shortcoming in the program's design.
Detail:
You want to learn the allocation requirements of a thread on your target architecture/OS, as well as keep your threads relatively busy/avoid polling, and to configure priorities correctly if you really do have a lot of threads. 'Many' threads may be 8 (or fewer, if busy), or 100+ if they have relatively little work to do, it ultimately depends on your needs and design.
As tests for some tests/objects/operations, I have used more than 100, and occasionally more than 1000 working threads. No explosions happened, though I have never had a true need for those operations to be that parallel in a shipping app (unless the aforementioned programs are being used in very unusual circumstances), and it made more sense to put the actual implementation into some centralized task manager. If you have time-critical/real time applications, then these tasks may be best on another thread. If they are short lived, consider a thread pool.. well, there are many ways to attack many problem classes...