Yes, just put the same code on each page, and the like code picks up the URL, title and description automatically.
my main question is why Facebook requires me to link it to an app? I simply want to place a "Like" button on each page - not link to any applications? :S
The button code needs to link to some kind of app that handles all the Like functionality. However, there are some arguments for not using "Likes", but rather encouraging people to share your content on Facebook, which is slightly different. Because I didn't want a whole bunch of JS and apps on my site, I just stripped down the buttons to simple HTML code that gets the same result (not a like as such, but a sharing of content). For example, you can just put a link like this on each page:
<a href="http://www.facebook.com/share.php?u=&title=[title]">Share on Facebook</a>
You just have to replace with the page URL and [title] with the page title. There are various ways to do that dynamically, especially if you are using a CMS like WordPress.
If you are interested, I wrote a little piece on this a while back. It's pretty basic, but still fun.