Free Online Games/websites for Toddlers/Preschool Ages

http://www.bbc.co.uk/schools/laac/numbers/chi.shtml
http://nlvm.usu.edu/en/nav/frames_asid_169_g_1_t_2.html?o...
http://www.abc.net.au/countusin/games/game7.htm
http://www.literacycenter.net/lessonview_en.php
http://pbskids.org/lions/games/flood.html
http://www.readwritethink.org/files/resources/interactive...
http://www.roythezebra.com/reading-games/capital-letter-1...
www.starfall.com

www.khanacademy.org (for any age, kids and adults). awesome site.

http://www.bbc.co.uk/schools/typing/ (free site to learn typing. Good for kids to learn, already).

All these sites, are good for learning, and is per my daughter's 1st Grade Teacher.
You can use these sites with any age.

I downloaded Kidzui to my computer. It's free and it takes over your whole monitor so the kids can't accidentally click on other things. It has links to almost all the kids games websites. I know it has Starfall, NickJr., DisneyChannel. It even has a link to YouTube. The best thing about it is that they only let you access games and videos that have been approved for children. So, the YouTube videos are babies laughing, or animals doing funny things...nothing you wouldn't want them to see. My son just turned 3 in March and he knows how to open the program and can navigate through it really easily.

uptoten.com --my favorite, tons of free online games and they organize them well, sprout, fisherpriceonlinegames (not sure if thats the site you can google it) scholasitc, my daughter has a bunch saved on the favorites bar and can go in and use it on her own, I've been doing that since she was 2, so I'm sure your 2 year old would love the freedom and games occasionally, also if you google dinsey princesses, dinsey has games too

I want to second starfall.com. Wonderful site! Also, if you go to your library's website they usually have links to websites with children's games.

www.disneyjr.com
www.pbskids.org

Have you tried www.zoodles.com? It is a kid based Internet program, you sign up for a free trial, after so many days, the free trial ends, but you can still access most of the stuff. They have where you can pay for "premium" service, but it is really cool. They have age-appropriate games, links, and everything, and they even have a place where you can read a story with a microphone hooked up to your computer, and later the child can click on the story, and have it read back to him/her. My mom who lives 200 miles away reads them on her computer, and sends them to my daughter, so she gets to read her stories. My daughter loves it!!! It will also "lock out" inappropriate websites. the children cannot access them.

Highlightskids.com (based on the magazine) my son loves the building games.
Disney Junior
Hit Entertainment