Puzzles come in various shapes and sizes. There are lots of puzzles for various age groups starting from kids as young as a year and a half. These are basic puzzles which involve few pieces, typically inserting them into slots onto a wooden board. As your child grows, you can introduce him/her to the more traditional and sometimes, complicated puzzles. Learning can be made easier with puzzles.
Alphabet and number puzzles are very popular with this age group. Floor puzzles with large pictures are a great buy too. I wouldn't recommend puzzles with a high piece count for younger kids. It can get intimidating if they are not able to figure things out.
Older kids, aged 5 and up are at the right age to start doing bigger puzzles. Then again, it depends on the capacity of the child. It's best to start off with a smaller puzzle and work your way upwards, as your child feels more and more comfortable with the puzzle making process.
Puzzles can be a very though provoking activity for the whole family. It's such fun to solve puzzles together, not to mention a great family bonding experience.