I have been using Conceptis Puzzles (conceptispuzzles.com) since about 2008 and I LOVE it. They offer various tutorials and weekly puzzles in about 13 different categories (Sudoku, link-a-pix, and mazes to name a few), and are always working on additional puzzle categories. They range in difficulty from very easy to very hard. Every week, each category has 6-7 new puzzles to complete.
Back in '08 when I started using the site, everything was free. Earlier this year the site moved to a subscription format, where you could buy "credits" to buy puzzle packages or single puzzles. A lot of people complained. Not me. The puzzles they offer now that they have a revenue stream are more challenging, more frequent and abundant, and I am able to do all of them online (I used to have to print some of them out to complete). The pricing is not that expensive either. I paid $12 for 1250 credits and I have yet to run out.
Conceptis allows you to play all of the tutorial puzzles for free, which in itself could take a few months, if not more. Then, if you do register for the site (also free) you get 500 credits free of charge. With this, you can buy all of the puzzles for two weeks, or single puzzles over an extended period of time. On top of that, the site offers one new puzzle each week free of charge, so you could potentially use the site and not pay a dime. The only benefit of buying credits is being able to play the puzzles that are not free, and saving them to your account forever.
I'd definitely recommend this site to anyone looking for a great puzzle site. It's kept me entertained for almost 3 years, and I hope it only continues to grow.