I want to have one object of some .NET class used by multiple processes on same computer.
Having Application domains, it is not easily possible to move across that boundary, but memory-mapped files in .NET 4.0 should ease that task in some way.
Until .NET 4.0 comes in final release... Is it possible to make some kind of "inter-process singleton" in C#?
Yes you can create a .Net Remoting singleton in one process, and expose it to the other processes running on the same machine via Remoting...
EDIT: in .Net 2.x, you need to use a Remoting solution, but in .Net 3.x or later (wherer WCF is Available) this same funcctionality may be available using WCF (Check it out)...