I myself have a Photo Trimmer that has an interchangeable cutting head, which not only includes a straight blade, but includes a blade that can create the perforated cuts in paper (like how you have a paper bill that you can pull apart, or like the stub and an airplane ticket which can be separated) and a "postage stamp" blade (which creates the edges of the postage stamps). It even has an LED light in there so to light the paper underneath for a clean cut. I picked it up from Big Lots for only $10.
Normally, when I need a really close cut (like when I needed to make four full size movie poster replicas for a classmate's short film), I use a metal ruler and an Xacto knife.
I also have a laminator I picked up from a K-Mart that was closing down, that I got for half the price (I got it for $12), but I haven't really had a real need to use it (as I haven't had a need for an ID prop for a short or a replica ID I could do, though I know there are a lot).
I also have heavy weight cardstock and some HP Desktop Inkjet paper.
Most of the paper prop creation I do uses Photoshop to create (such as the BSG paper prop replicas I've posted and the Wanted poster for The Terminator).