Gaming 100: Two Online Games for Toddlers to Get them on the Road to Gaming

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The conundrum I have been wrestling with is how am I going to turn a toddler into a gamer.  I started out slow with the basics - Sonic, Mario, and the Monkey Ball series but her hand-eye coordination wasn't up to par yet.  So we moved on to online Flash games.  Here are her two favorites that I recommend for anyone with a toddle to not only occupy their time but to start laying the groundwork for the future gamer in the family.

Kindergarten.  It's 'The Sims' for kids.  You act as a teacher of a kindergarten class (even though the students look a lot more like they are in preschool) and do very 'Simmish' things including changing them, feeding them, playing with them, sending them to bed, and bathing them.  The whole concept however not only cracks my daughter up but also empowers her to take care of the 'babies' instead of being one.  The only downside is that 9/10 times I have to do the operating since it requires a bit more hand-eye coordination than other simple point-and-click games.  However, the positives definitely outweigh the negative.
NOTE: There is a pay version of the game that gives you more options.  I never paid for it so I can't vouch for the money and whether what you get is worth it.  I just play the free version and lose my progress after a week or two (after all it is not like it is real intensive).
http://www.miniclip.com/games/kindergarten/en/

Dog's Day Out.  This game is great stepping stone.  Like many current games, you get to customize your character (the dog), and the jump is the most important part.  Your dog runs through the park jumping over obstacles and jumping to catch bones and frisbees thrown their way.  The major advantage of this is that it only requires the space bar to jump so my daughter can do it completely on her own.  She had been able to play this since just over 2-years old.  It gets some basic, much needed, hand-eye coordination down and also teaches the fundamentals of some of the simpler action games - including timing.
http://animal.discovery.com/pet-planet/dog-parks/dog-park-game/