As I always say with this type of anime that involve love.... opinions are really subjetive, cause honestly, love is one of the most subjetive things on the world. That said, I think this is the best romance anime ever, and for many years has always been my favourite anime of all time.
The strongest part of Toradora! are the characters. Every character is really, reaaaaaally well done and always have a real and logical/coherent way to "do what/act how" they do. I have seen a lot of anime, and there is a lot of them were sometimes certain characters act or do things really different of what you would expect based on the personalities they were given, just to make certain situations more dramatic or whatever. After having watchet Toradora! several times (too much probably), I can definitely say their characters feels very coherent and real, and that helps A LOT to make the plot really touching.
Aisaka Taiga, the main female character of Toradora!, is what people would usually call a Tsundere. But contrary of what a lot of people think, being a tsundere is not about being really aggresive and kicking everyone asses at all times. I think Toradora! explains really great through this character what a tsundere really is and why is that they are like that.
A tsundere is a really really shy person, so shy that he/she act aggresive to "evade" embarrasing situations. A lot of time they don't even like/want to be/say those aggresive things, they even think the opposite (Note: Read Vanilla Salt -1st ending- english lyrics). Tsunderes are so shy they just can't avoid to run away of embarrasing situations, they get embarrased so easily, even if you tell a Tsundere he/she is really good at something, or cute, they will get embarrased and will say something aggresive to end that situation. They can be really glad, or even want to say "you too", but they are too shy they just can't, they are not capable of saying what they want. Pretty often tsunderes hate being it, they want to say one thing but they just... they can't. They really want to be more open, but they are so extremely shy they struggle SO much to be like/say what they really are/want.
Also, tsunderes don't even have to act violent or aggresive, they can also act confident, or even funny. It's just that on anime they usually act violent, and also cause when a tsundere acts violent is more noticeable that when, for example... Okabe Rintarou acts crazy/funny. Cause yea, Okabe Rintarou is tsundere too. Bet a lot of ppl dissagre/didn't notice that. Also this may sound weird but, my source is really good I would say cause... I am a bit tsundere too IRL xD That's why I understand really well characters like Taiga and other tsundere characters.
Toradora!'s plot is basically their characters. Their feelings, their mistakes, their struggles.
Takasu Ryuuji, main male character, has a crush for Kushieda Minori, and his best friend is Yuusaku Kitamura. Both Minori and Kitamura are in the same class with Ryuuji. Ryuuji's hair/face makes him look like a bad guy to others, so he really doesn't have that many friends besides Yuusaku Kitamura, and always has problems with his look even when he is a really good person.
Aisaka Taiga, who is also on the same class, has a crush for Yuusaku Kitamura, and her best friend is Kushieda Minori. She is a tsundere, she is really agresive so she doesn't have that many friends either besides Kushieda Minori.
There are more important characters later, like Kawashima Ami, but those ones are the starting point of Toradora!.
So, since they get to know their crush is the other one best friend, Ryuuji and Taiga decide to help each other with that. That's it, can't say more! A lot of things happen, a lot of things change... you get to know every character on detail, and will love them, I promise! So go watch it already :)
Edit: Several typos :P