iMac 27 inch with apple care, worth or not?

Yes, it is good insurance to have.

It's always wise to buy AppleCare if for no other reason that you have years of peace of mind that if a repair is needed after the 1 year warranty you are covered. If you need one repair, in most cases AppleCare has more than paid for itself. In addition to the repair coverage you also get phone support. IMHO AppleCare is worth it for the phone support alone. Some will disagree with me, but even as an experienced user I still wish my computer was covered by AppleCare so I could pick up the phone and get questions answered.

BTW, as a student you get a discount on AppleCare so that really should make it a no-brainer.

There's the technical support and you can decide on that vs.using a forum such as this one where IMHO) people are going to be more prepared to do prolonged troubleshooting and maybe find solutions that aren't always by the book.

There's the warranty. For big ticket technology this is seriously worth considering. While you hopefully will not have problems there can be manufacturing errors with anything and we are talking expensive, sometimes cutting-edge technology with large repair costs. Can you afford $800 should something go wrong?

Still, check alternatives. For example, some credit cards will add a year onto a manufacturer's original warranty if you use a card to pay entirely for an item. This won't include call-in support like full Applecare but if you don't need that but would like a bit of added warranty coverage that may tip things the other way for you.

When my wife bought a Mac computer we bought Applecare for it. When she bought an iPhone we did not (she is very careful with it and not a stick-it-in-your-back-pocket kind of person). iPhone Applecare is only for an added year and we bought it with a credit card. iPhone repairs aren't as costly. iPhone Applecare was going to cost a significant % or what it would cost to buy one new and iPhones really only have a practical lifespan of 3 years anyway, so if something happens in the third year just buy a new one.

In 30+ years of owning Apple computers I've not had many need work, but it is still worth it IMHO. If you sell in less than 3 years it also stays on the machine and is a good selling point.