Hello!  I feel reference checks are an old-school practice.  There is no way to 100% guarantee the validity of any person offered as a reference for a candidate.  In addition, there is the legal risk of someone providing false information on a candidate that leads to an unfavorable hiring decision.  Libel and slander are real.  As an alternative, I like to have candidates shadow the role and organization.  Invite the candidate in for an hour or two and ask them to sign an NDA.  Being able to experience the position, even briefly, can be very beneficial on both sides.  

Yes, they are worth it, if you are intentional about who you contact and what you ask.  I don't call the "references" the candidate lists, because I already know they'll say how wonderful this person is.  I contact previous employers and try to speak to the person who supervised the candidate, but often speak to HR.  At a minimum I verify that the candidate held the job they listed, for the amount of time they say.  I ask about attendance, ability to work with others, quality and quantity of work. etc.  I have found out that a candidate only worked 2 months at a job they say they held for a year, that they had trouble getting to work on time, that they missed deadlines, or that the job just wasn't a good fit for them.  Sometimes I hear that there were no issues, or that they wish the person would have stayed longer.  If the person I speak to gives false information, the legal risk is theirs, not mine.  And I have been lied to, but typically in the form of a glowing reference for a poor employee. 

I haven't found them useful outside of verifying dates of employment and title. Very few people are going to list references who wouldn't speak highly of them. Additionally, if a company requires a certain number of references, and the recruiter/hiring manager doesn't hear back from one or more reference, you risk slowing down the hiring process, and thereby losing out on a potentially good candidate.

If you asked this two months ago, I would have said I thought they were worthless. Pretty much everyone has three friends they can list. However, I was recently surprised at how candid the last batch of references I called were. I have not found this to be a typical experience, but I did get useful information from those calls. If I made the decisions, I'd prefer to run a background check and to forego references, but I think there is no right or wrong answer as long as you are consistent in your process. I do both at the request of my employer. I make the offer "verbally" or by email stating it is contingent on a successful background and reference check, send the authorizations to check, run the check, and then send an offer letter to finalize the process. Hope that is helpful.