Reference checks are rare, happened to me only once. They will call your previous manager and talk about you, so make sure you've left on a good terms. They do it before extending an offer, so you can just tell them something like "thanks for your time, but another opportunity pop up".
Other thing is background checks. These happen quite often after the offer is extended. These aren't problem unless you've lied on your CV or commit felonies. In this case offer is legally binding and they can't rescind it unless some hardcore stuff pops up.
Some times they do it only for looks. Once Ice signed background check form with scary warnings like "lying on this page is a felony under yada-yada law", they did not check shit there. I know.