How can I make Plants vs. Zombies not pause whenever I switch windows?

With all of PopCap games, it's not possible. Their 'framework' includes pausing when away (ie window not focused). I agree it's inconvenient for these cases where you have to wait until the end of something.

Maybe one could make a tool to fake focus in Windows? It's technically feasible to make a program change the active window of the OS.

Anyway, I think you have to find applications that you can open before PvZ, and that you can use without focus (ie open a webpage on the available desktop space - as @Sorean said, more than one monitor helps).

I can remember someone addressed this with a virtual machine using VMWare.

Not the best option, but it is possible anyway.

Unfortunately no, it's an "active window" type of game where your current focus needs to be on that window. The second you click out of it, it will pause for you. Kind of a built in safety in case you click away at a key moment in time.

I hear what you're saying though, it does kind of suck that you can't. I find dual monitors helps a lot when I'm watching something else on the other screen (back when I used to play it).