(UPDATED 2019) I've had many people over the years ask me what to look for when purchasing a good laptop.  That has changed over the years as we have seen a shift into multi-core computation and reliance on SSD technology.  So, here is a current run-down of buying tips (in order):

  1. Buy just inside your budget, but do spend as much as you can for it, since that will probably make it last as long as it can for you.  Buying the cheapest means you'll likely need to replace it earlier.
  2. Memory:  If you are comparing multiple computers, at this point go with the one with the most RAM.  8GB is standard now for mid-level laptops, 16GB is even better.  2-4GB is doable for chromebooks and it works for a netbook, but it's not good for doing anything "big" on the computer.  (For any real work I use my desktop or laptop with 16-32GB of RAM each).
  3. Cores: The next thing to look at is the number of cores in the processor.  It goes hand in hand with the RAM, in that you want as many as possible.  In the worst case I'd trade off more RAM for fewer cores.  This information would likely be in the fine-print of the computer details, but it will say "x-core processor." I'm not too worried about the brand (Intel or AMD) at this point.  Typical low-end laptops/chromebooks have 2 cores.  For longevity, I'd go for at least a 4-core if possible. (The best option now would be 4-core "hyperthreaded" which means it works like 8 cores. You will find this on most Intel processors.)
  4. Type and speed of processor:  This is secondary to the number of cores, mostly.  Intel has the reputation of being the best, but AMD has a new line of processors that are supposedly awesome.  However, in general, AMD's processors are cheaper to buy, giving you more options in the lower-cost machines that could potentially be "faster" than their Intel counterparts.  (For desktops, I buy AMD to get more cores and speed for the price).  That is to say, after RAM and number of cores, I'd pick an Intel i9, i7 or i5 line over the AMD chips (A-series processors), but I'd pick AMD's A10, A8 over the Intel i3, Pentium, Celeron, or Atom models.  At this point, don't buy a laptop with an ARM processor (that day is still coming).  Secondly, get the fastest processor of the best line you can (higher GHz).  Since the multi-core revolution, I'd say number of cores wins over speed of the core, since it allows the machine to do more at once, even slowly.
  5. Hard drive: SSDs are faster. Period.  Do not get a laptop anymore with a rotational hard drive (HDD). SSDs are prevalent and the prices have come down significantly, so you should get a laptop with and SSD in the size you are looking for. 256GB would probably be the smallest I'd suggest, especially if you are using Windows.
  6. Brand: Last but not least, get a brand you know.  Apple is known for its customer support, and I've had wonderful experiences with them. Dell, HP, and Lenovo seem to be the go-to PC brands, and they've been around and solid for a while.  Asus and Acer are also great brands.
  7. Weigh the costs of getting an extended warranty (i.e., Square Trade, Geek Squad, etc). Many PC manufacturers will force you to pay shipping to have the laptop sent for inspection, then deciding whether it's a free repair (but you still pay shipping) or a non-covered issue where you pay shipping and repair costs. Some warranties may be worth it, but I haven't used them. Apple's AppleCare+ has been worth it every time I've bought a Mac/iPad.