i guess u can have as many as u want, depends on how many ports like USBs and FWs and express cards u have.. + it also depends on how strong your computer is.....
The main thing is that this is not an easy question to answer. Theoretically, VJQuark is right and Resolume can handle as many inputs as the system can recognize. Aside from straight USB or Firewire connections, you can also get input streams via PCI and ExpressCard connected capture cards. So it's pretty much limitless.
Practically, we've had reports from users of certain type of (cheaper USB) cameras 'locking each other out' so only one can be used at the time. Also after a certain point the performance will go down, because too many streams have to be processed at the same time.