Well Windows Live was supposed to do this, and yes it's technically possible for Windows users and Xbox users to play each other on Live.
With today's consoles, this is barely more difficult than getting a flash animation to work on both Safari and Firefox, or a Mac and a PC, but the real obsticle is whether or not companies want to co-operate. Does it benefit MS in anyway to allow PS3 users to connect to Xbox Live and play CoD4? At this point no, because the biggest selling point of the Xbox360 is the online community, via XBL.
Additionally, there is a difference between MS' and Sony's approach to online play. MS supply XboxLive to all developers for all games, and it works basically the same way for everyone. The downside is that users have to pay for it. Sony, however, asks developers to provide the infrastructure for their own games and absorb the costs themselves - although this model is slowly changing.
Finally, piracy in the PC market means that not enough money gets to the developer or publisher to pay for an infrastructure like Xbox Live.
So yes, it's possible - it just requires developers to release compatible netcode and make the servers available to all - but it's unlikely this generation.