I remember that, at the time, Gaara was my favorite character. So his fight against Deidara gave me some damn chills, as it was life or death, and I really believed Gaara would be dead for good if he lost.
Jiraya vs. Pain gave me chills, especially in the Video Game, where they changed the end of the fight so that Jiraya throws a last MASSIVE rasengan in Pain's face.
Kakashi vs. Pain. Man, I was SURE Kakashi was dead. Though everyone called BS on Nagato using Rinne Tensei to bring everyone back to life, I really liked it, if only for the fact that it allowed Kakashi to live.
Deidara vs. Sasuke WOULD have given me chills, if I hadn't been so sure that Sasuke would Plot no Jutsu his way out of a CERTAIN death.