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Does the genre matter? If no I'll list what I know:
From ongoing series you could try Magi which are fantasy action series. Morgiana is a great character who starts as slave but then gains freedom and does everything in her power to help. From side characters Ren Hakuei caught my attention. She is a strong and rightful as well as fearless leader of a country who will do everything in her power to keep peace.
Angel Beats! - character Kanade really caught my attention. At first she is a mystery but later we start to learn more about her. Series are comedy/drama set at school setting.
Chihaya from Chihayafuru is a good choice. She is a teenager who spent most of her childhood admiring her model sister. One day she finally discovers something she becomes very passionate about aka Karuta. Since that moment she does everything in order to promote Karuta and become better at it. She does not plan to give up easily.
Ga-Rei: Zero - something more dramatic and action orientated. Yomi is an excellent character, probably the most memorable of the series. To be honest, if not her I would not like the series as much I did. She is strong, beautiful and carrying but sadly life decided to be nasty to her... You might get disappointed with her at some point but in the end you still will admire her and feel sorry.
Series show future events first and then go into flashback to show how we got where we are.
A bit more gory series.
If it's fine, in this case I would like to recommend manga... Series are called Love Hina. Anime is not bad but it misses lots of material and does not develop the character properly. The one I'm talking about is Motoko who is kendo student and hates males. She also is not very feminine. But she is strong and determined. Out of all anime/manga I've seen her character probably develops the most and you can't not like her. For me she used to be a real model because of how much her tomboyish character reminded me of myself. If you compare her at the start and the end of the manga, it is almost like a different person yet she still seems the same. It is really hard to describe.
Homura from Madoka does deserve admiration too. She seems cold at first but once you learn her back story you just can't not like her at least sympathize. She went through a lot and I would love to have a friend like her.
Mmmmm, duno if it will work but maybe The iDOLM@STER? Series are lighthearted and mostly episodic but it has one very memorable arc and character. The girl seems distant and cold and at first make you dislike her. Gradually you start to learn more about her and the problem and when it finally comes to conclusion you can't help but be happy for her and admire her.
I lost count how many people said that they cried at episode 20. I defiantly had several goosebumps. Episode 21 is a nice follow up and conclusion to her story that strengthens admiration factor.
Hope some of them will work for you.
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