Hi - lots of ideas and suggestions below from other moms. I agree that PBS and NickJr offer some of the best kids programming, as well as a few things on Disney. I just want to add a few of my thoughts and give you my "list" of TV shows to complement your other advice. My daughter also had no TV or videos until after she was 2. I never did Baby Einstein or any of that off the shelf stuff either, and still only have added a few classic movies (after she was about 3.5 yrs old...I'll mention those at the end).We basically read, read and read and showed her places, things, etc. by going out. So,by two we were all ready for a bit of TV! :)
Looking back, there were just a few shows I found good for my daughter at 2. Many of the ones mentioned below, like Backyardigans, Sid The Science Kid, while great shows are really for kids a bit older - over 3 in my opinion. You need simple, fun, focused, repetitive, shows that do not overstimulate. Also, short episodes are good. There is a good reason why kids love DORA at this age - it's simple, and fun, and it is educational. My daughter seemed most interested and positively stimulated by Dora, Caillou, Blue's Clues, Max & Ruby, Disney's SuperSleuths, Barney, Bob the Builder. Then as she grows a bit more or you can sense she's moving on Franklin, Little Bill, Dragon Tales,Clifford and Handy Manny, Miss Spider's Sunny Patch are nice shows with good values mostly about friendship, family and doing the right thing. Often kids grow out of Dora and right into Diego - I can't recall how old my daughter was, but perhaps about 3 when she was all about Diego!! Then as she's 3-3.5 you can also add shows like Super Why!, Word World, Lazy Town, Reading Rainbow, Backyardigans, Little Einsteins, Sesame Street (if you didn't add before - my daughter didn't watch it very much until after 3). Lot's of good kid programming these days. Make sure you watch the shows with her at first especially - doctors say interaction is key and that's why Dora and some of the other shows are so great - they get the kids interacting with the content. You can speak with her about the show, what's happening, how the characters are feeling, why, etc. You can also guage her real interest and modify your selections accordingly.
Last thing I would add is that I would recommend determining your rules around TV and keeping consistent with those so as to create positive TV watching behavior. For example, we started off watching 1 show after breakfast in the mornings, and one show in the late afternoon after her nap. Since we were consistent, she didn't whine about turning off the TV and she didn't bug us to turn it on during other times of the day. Then as she hit 3, we changed that to two shows in the am only after breakfast (and after brushing teeth!). Now at 4 she gets to watch 2 or 3 episodes in the morning. And on days she doesn't watch am TV (such as preschool days) she may watch a couple shows in the afternoon, after her naptime. She does not watch TV after dinner or before bed except special occasions (like at Christmas we all watched the Grinch Who Stole Christmas together). As the experts say, we found late evening TV winds her up. We stick to playing a game together as a family after dinner (such as Candyland, Go Fish or something) and then bath and books.
As for movies, we didn't do any feature movies until she was a bit over 3 years old. Some of the movies we find she very much enjoys (and which we are OK with her watching now) are: Charlotte's Web, The Land Before Time (and related short movies), 101 Dalmations, Jungle Book, Aristocats, Pinnochio, The Grinch Who Stole Christmas. Now that she's almost 4, she really likes Chitty Chitty Bang Bang (but it's long!!), Nemo, Monsters Inc. Also she enjoys the Disney Princess Enchanted Tales short-movies that send nice messages about perseverance, courage, etc. She's not a realy "princess" girl in general, but likes those stories.
Hope that was a helpful addition to all of the great advice you received. :)
ON A RELATED NOTE: If you are interested in reading a good book about how children learn, there is an excellent one written by two mom PhDs on this topic called EINSTEIN NEVER USED FLASHCARDS. Super read and very interesting.