Well, the big obvious one is that it voids your warranty. No manufacturer will offer you support or warranty service if your device is rooted. Telecom companies might, mostly because they don't care and the workers they employ don't know better, but if you want support from the people who made your phone, you'd be out of luck.
Another disadvantage is that you would no longer get OTA updates. By rooting, you exclude your device from the automatic system updates that get pushed out. You can still apply these updates manually, but it requires a few more steps and can be a hassle. This is less of an issue because most people who root their phones use custom ROMs that don't get official OTA updates anyway, but if you're using stock Android and you want to keep up with official updates, you'll have to do it manually.
You also place yourself at risk if you don't know what you are doing. Root access grants you a tremendous amount of power but it leaves you vulnerable. You can very easily brick your phone (render it useless) if you accidentally alter the wrong system file. You get a lot more customization options but you also wind up with a lot more ways to turn your phone into a paperweight.
There are other disadvantages and risks, but they are less directly related to rooting and more a result of things that you can do WITH root.