I got a reference on my first job. Now I was asked to go to an interview. Should I take a copy of the reference of the first place to the interview even though the interviewer did not ask for it?
It can't hurt to bring it a copy of your references or their contact information. Somebody might ask for it, and instead of saying I will get back to you, you will be able to give it to them right away. I have also run into the situation where they want me to fill out a "application" before I leave, even though they have my resume, and I have completed forms online. Having the copy of the reference makes it easy to fill in that section of the application.
I always bring extra copies of my resume. You never know when somebody might not have one, or when the system they use for interviews produces a unusable one.
I also bring questions I want to ask, and notebook and pen to make notes.
While mhoran_psprep is correct in saying that it can't hurt to bring this information and it may show that you've come prepared, I'd be very hesitant to provide information on my references at what seems to be the very first step of the hiring process. You typically do your references the courtesy of informing them that someone from Company X may be calling them because you're applying for position Y. You're talking about people's communication details after all and you don't want to give those out too readily, even if there's usually no reason to think someone might abuse the information.
A lot of employers ask for reference detail up front to streamline their process and because it doesn't cost them any extra effort. Because of that it's equally common to dodge that question or fill in "available on request" if there's an online submission form you need to get through. Don't ever add this to an application otherwise though, it's understood that you'll provide references if asked for them.
So since you shouldn't be providing references at such an early stage of the process, I probably wouldn't bring this info on paper. It makes sense to keep a digital file of your references though and you can always bring that just in case you're asked for them and you feel like it might be useful to make an exception. I'd never volunteer this info myself: a prospective employer will ask you for your references when they're ready for them and it makes sense to let them control the timing of that part of the hiring process.
Think about these four questions to come to a logical conclusion. This doesn't work in all situations, but in this particular situation, I believe it will.
What is the worst case scenario if I do bring it?
What, the potential employer complains about you cluttering his desk? Seriously, there is absolutely no harm in bringing it. The worst that can happen is that the potential employer say, "Oh, I already saw that, you can keep it."
What is the worst case scenario if I don't bring it?
Obviously, the employer could ask for it, and you will look unprepared if you don't have it with you.
What is the best case scenario if I do bring it?
Best case is if the potential employer wanted it, and you have it. It gives the impression of being well prepared, as well as giving you a head start on the possibility of a job.
What is the best case scenario if I don't bring it?
Well... nothing, really. There's absolutely no advantage to not bringing your references with you.
Just those four questions I believe answer your question. Yes, bring your references: it doesn't harm, and it could help.