Yes, absolutely. I had a diamond membership, and it was great. Chess mentor is great, and the videos are good. I will upgrade again when funds come availiable. All you need to know... look at all the repeat premium subscribers. You can play for free all over the internet, obviously, there is a reason people choose to pay to play here.
Premium Membership, worth the price?

Have you availed yourself of the free 10-day premium trial? You'll be able to judge for yourself afterwards.
the free trial pops up when you first get an account. Sadly, you only have about 48Hr. to accept the offer.
http://www.chess.com/membership.html
I was given a free week of diamond membership, and I would say the Chess Mentor, unlimited tactic trainer problems, and computer analysis would be worth it (this was what I used). You also get videos/tv and an archive of your games which was nice to compare my chess skills now to when I first joined the site.

Yes, the full archive of your games is great to have.
Much better than the last 30 days worth or whatever you get for free.

the free trial pops up when you first get an account. Sadly, you only have about 48Hr. to accept the offer.
It was my experience (before I paid) that the 10-day offer reappeared after a couple or three months.

As of now im a basic member and get one computer analisis per week. I must say, it was really neat to see how the computer broke down my game.

Can I get my money back on the 30th day, sign up again and repeat?
Not that I would ever do such a thing!
Honestly though, for about 25euro a year you can't go wrong. And before I went premium some of the pop-up ads used to break the page on me so I'm doubly glad I upgraded.
the pop up adds can be very annoying. This is off topic, but I just realized that Erik has 10,000 points!
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I have noticed that chess.com advertises premium memberships a lot. Chess mentor and the exclusion of adds would be my main incentive to upgrade. However, there is a price. Is it worth it?