Fun Puzzle Websites

This is nowhere close to a complete list! There's so much fun stuff out there!

Oregonian's Puzzle Kingdom: Lots of logic puzzles of all sorts, including Battleships, Sudoku, Pic-a-Pix, Kakuro, and Hashi.
Maths Resources (the British call it maths): Dozens of fun puzzles and games, including classic card and board games as well as newer online games like 2048.
KenKen: Includes various difficulty levels. Great practice for thinking about numbers (especially factoring) and logic!
Numbrix: another neat logic puzzle. Try the easier levels first to get the hang of it.
Brain Teasers from the National Council of Teachers of Mathematics' Illuminations website
Calculation Nation online math games (also from NCTM)
Hotmath math games are at various levels; pick one that is appropriate for you (the cockroach one is pretty funny)
NRICH Enriching Mathematics: Lower secondary is probably the most appropriate level here
Vi Hart has a lot of amazing videos on YouTube. I haven't watched all of these, and some rely on high school or college math.
Lure of the Labyrinth is a computer game designed for pre-algebra middle schoolers. It has a storyline in which you are rescuing a lost pet from monsters in a labyrinth by solving complicated math puzzles. You can set up a free account to try it. I have not investigated it much yet. If you try it, let me know what you think of it!
Lewis Carroll Puzzles: How can you go wrong? I also strongly recommend reading Alice in Wonderland and Through the Looking Glass if you have not already!