When my daughter turned a year old, we decided to buy her some building blocks for her birthday. We had noticed that she was getting very good at handling things and stacking blocks so thought it would be a great gift. Boy, were we right! Out of all the toys we've ever purchased, I believe this set of blocks has gotten the most use by far.
These blocks are sold in bags of 100. They look like legos but are a lot bigger and easier for small hands to handle. My one-year old daughter was able to stack these on top of one another very well. Now she is 2 and a half and still uses them (as does my 1 year old son)- but now we try to get her to recognize the colors (red, orange, yellow, blue, green) as well as how many holes each has.
These are made of plastic and my kids play with them in the sandbox, bathtub and playroom. They are virtually indestructable. The carrying case is zippered, which helps keep them concentrated in one place, and actually makes cleaning them up fun (they get to zip up the case and carry it by the handle).
Since buying these I've toyed with the idea of buying another set. They do tend to disappear so the buildings get smaller all the time. I've also purchased these for my friends' children who have told me how much their kids like playing with them.
Overall, I highly recommend Mega Bloks for the toddlers in your life.