There are many times that I did all the thing that I had needed to do and for the rest of game I just need to wait and watch the game will it ends. Isn't there any way to I could switch to another window and let the game continue?
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).
If you're only wanting to context-switch onto your other window in order to scroll a strategy guide (or Arqade question, ha), then a possible workaround is to install a tool that allows you to scroll the other window, whilst leaving Plants vs. Zombies as the "Active" Window.
I have used two tools in the past that do just this:
...a mouse enhancement utility that makes your mouse wheel work on the window currently under the mouse pointer, instead of the currently focused window. This means you no longer have to click on a window before being able to scroll it with the mouse wheel. This is a far more comfortable and practical way to make use of the mouse wheel.
...[enhances] the functionality of mice with a scroll wheel, offering "universal" scrolling: moving the mouse wheel will scroll the window directly beneath the mouse cursor (not the one with the keyboard focus, which is default on Windows). This is a major increase in the usefullness of the mouse wheel.
Whilst you will still need to click in order to change windows, click hyperlinks, change tabs etc, this will at least allow you to scroll the current page and continue play at the same time.
NB: Personally I prefer KatMouse as it seems a little more lightweight, but both do the job admirably.
Sorry if I'm a bit late but there is a way. You can go to steam and press add a non steam game. Once you've added plants vs zombies to your games list hit play from there. then once you've setup your defense you can press shift+tab on your keyboard and press web browser on the menu. Hope this Helped! (writing this answer from steam lol)