Wood is a great material for lots of things, but if you want to put it in your kitchen you should be aware that it requires regular maintenance and has several limitations.
Wood does expand and contract with temperature and humidity, but if it's properly finished (on both sides!) and fastened in such a way that it has a little breathing room, that shouldn't be a big deal. There are lots of large pieces of wood furniture (e.g. dining room tables) that survive just fine without warping or cupping.
A bigger concern is waterproofing, especially if you're going to put the wood counter near water, like around a sink or above a dishwasher. The wood needs to be kept well-oiled—at least several times a year you will need to oil it to keep it in good shape, maybe even once a month, depending on its condition. You know the wood is oiled enough if you can splash some water on it and the water beads up. If the water seeps into the wood, the counter isn't properly finished and will rot / mold / stain.
In terms of general care, wood doesn't do well with pools of water or spills sitting on it for a while, and of course it can be marked by knives etc. If you can live with regular maintenance you should be fine, but you have to be honest with yourself about whether you're willing to take on the responsibility. You can't just let a spill sit there for a while until you get around to cleaning up.
Personally I might use wood counters for part of the kitchen—maybe an island or general prep area—but not around water.