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I have Geek Squad Protection on my phone and they told me that a rooted device was covered by that warranty also so I just rooted today just one week after getting the phone.
It really depends on the agent who you take the phone to, if you have a problem.
BBY - If I root my Samsung Galaxy S3, will that void the... - Best Buy: Unboxed
They "should" cover hardware issues regardless of whether the device is rooted or not, but if there is a software issue or if you brick your phone or any such thing, it is unlikely that they will cover it.
Having said that, as long as you are reasonably careful while rooting (make sure you read/read/read and read some more before you flash anything) - read the threads, check that you are downloading the correct version of the software for your phone/firmware, it is unlikely that you will damage your phone beyond recovery.