Eh, HR at previous employers might share whether you were a problem employee. And any references you provide from previous employers had better speak glowingly about you -- if they wouldn't, don't provide them.
I don't know if any of the references I've ever given were called, but since none of the references I've given ever told me about getting called about me I assume none were called. To be fair I've had a) few jobs, b) enough credentials in terms of portfolio of public works (in standards setting organizations, in open source, etc.) that there is little need to check those references. If you interview me and you can get me to talk in detail about said public work and also you can check how I think and would solve problems, then between that and a background check that's almost certainly enough.
This is why I tell people to make sure to have a portfolio of public work. In practice it is difficult to make a large portfolio of public work -- at some point that has to include participation in the upstreams of external open source, in mailing lists, in fora, etc., and that all takes time and not being shy. Most job applicants are not going to have much of a portfolio.