From the person who simply needs to boil some water for tea, to the backcountry gourmet preparing a 3-course meal, there is a cookset for them all at a wide variety of prices.
Most backpackers I know eat rather simple meals, usually dehydrated or freeze-dried, and for them a small Titanium pot or kettle does the job of boiling a couple of cups of water. Titanium pots are very lightweight but are on the expensive side. If you're on a budget, a simple Aluminum pot from a Boyscout mess kit, or the infamous Wal-Mart Greasepot, may do the trick. If you're cooking for more than one person, you may find yourself needing a larger pot. If you're cooking an elaborate meal you may also need several pots, a skillet, or even a wok.
If you're actually cooking in the pot versus just boiling water, I'd strongly suggest you get a teflon coated or other non-stick surface pot as food sticks really well to uncoated aluminum or titanium. But whatever you choose, make sure the cook set you buy fits well on your stove. Most backpacking stoves, especially canister stoves, lend themselves well to small but taller pots.