I've often heard people explain that the best cat toys are cardboard rolls and ping pong balls. Turns out, we're finding that kids also like pretty simple toys.
I gave my two a couple of old foam camping mats and they love 'em. They have enduring appeal. In our house they are always referred to as 'cars' and you can even fit an additional passenger in one.
So, in this super easy instructable I am suggesting buying the cheapest foam roll camping mat you can find (<$10) and handing it over to your tiny child (ours have loved these from about 1.5 - 3.5 years old and counting - the eldest does not show signs of being bored by it).
We have other toys with electronic sound effects and suchlike but these foam mats are so simple that they fill in all of the blanks with their imagination. I like that.