Is there a dictionary app that I can just click on a word anywhere (in any app) and it will automatically define it for me?
With the release of iOS 5, this is now very simple. Dictionary functionality is available in any app that allows you to select text. Just highlight the text as if you were going to do a Copy and you will see a "Define" option next to "Copy". Tap "Define" and you get a pop-up window with the definition from the same dictionary built in to iBooks.
As mentioned by Alex, that is not a supported feature by iOS Apple, and I don't think there's any Cidya app that will add this functionality.
My favourite dictionary App is Dictionary.com:
There's a free version with ads, and an ad-free version for $2.99.