I am looking for a new laptop. It seems the best resolution I can get is 1366x768 on a 15" screen. I can find a 1600x900 on 17 inch screens.

My current laptop (Asus F3Jp) is running 1680x1050 on a 15" screen. The rated resolution is 1280x800 (http://www.newegg.com/Product/Product.a ... -_-Product)

How can I increase the resolution on a new laptop?

Are you sure those specs on NewEgg are correct? Unlike CRTs, LCDs are designed to run at one resolution. You can run an LCD at a lower resolution than it's designed for (albeit it looks like crap, the number of physical pixels on the screen remains the same, it just stretches the image) but I have never heard of being able to run an LCD at a higher resolution than the one it's designed for.