Quad-core processors: In the world of laptops, a dual-core processor is likely to be faster than a quad-core for most of the mainstream applications that the majority of users run; a dual-core CPU often operates at a much higher clock speed, and most general-purpose applications don't make good use of four CPU cores.
But if you do a lot of video-processing tasks, heavy scientific computation, or engineering work, four cores may be a great way to go. If you want to buy a future-proof desktop system, keep in mind that multithreaded applications are becoming the norm, and your PC will be able to hammer away at more tasks if it has a bit of extra computational headroom. Truth be told, unless you're looking at a particularly low-end desktop, it's difficult to find a desktop PC that isn't already sporting a quad-core CPU. Related: How to Upgrade Your CPU
Laptop display brightness: A bright laptop screen is usually one that drains the battery quickly. Besides, 300 nits is so bright that it's hard to look at indoors, and most users turn their display's brightness down a little anyway.
The exception? Display brightness is important for people who often use their laptops outdoors. If you do, you'll want all the brightness you can get. Related: Top 10 All-Purpose Laptops
Laptops and Desktops: Specs That Always Matter
Amount of RAM: No doubt about it, in any computer you're better off having more RAM. A netbook with 2GB of RAM will be a lot snappier than a laptop with 1GB. If you're serious about performance, don't settle for less than 4GB--and getting 6GB or 8GB of RAM isn't a bad idea. Related: How to Upgrade Your RAM
A roomy, 7200-rpm hard drive: Usually listed in revolutions per minute, "hard-drive speed" refers to how fast the platter spins. Faster-spinning platters generate both faster data-transfer speeds and faster seek times. A 7200-rpm hard drive will often produce a more responsive feel than a 5400-rpm hard drive will. Related: Top Internal Hard Drives