Contains spoilers. Your own fault if you read and ruin it for yourself.
The most memorable to me would be:
1. In the last episodes, they were all sitting in the train. Shizuru is reading the paper and suddenly she gaps, showing everyone the article about a "Three eyed short alien" a human saw.
That was so hilarious! I laughed myself crazy because of that picture of Hiei.
2. When the dark tournament dome was collapsing. Juri ran to Koto and begged to escape, crying that she doesn't want to die a virgin and Koto announced it all over the stadium
3. In the last episode, Hiei gave Kurama the tear gem and Kurama started joking and saying he's not interested in Hiei that way and values their friendship.
4. Finding out that Koenma's punishment is spanking!
5. All the heartmelting moments when Kurama changed into Youko Kurama...or whenever they showed a flashback of him.
Kurama
6. Kurama and Hiei laughing after Yusuke complained his "ticker ain't tickin right".
7. Yusuke telling the Spirit Defence Force he's going to kill and eat everyone and spead his evil rule and take over the three worlds
...then laughing his head off and saying it's a joke.
And then repeating the joke and scaring them some more.
8. Keiko slapping the hell out of Yusuke.
9. In the last episode when the two girls thought Kurama's a girl.
10. When the guy who got his strenght after drinking alcohol, started calling Koto Sheila and wanting to date her...and in the makai tournament when he fell in love with one of the fighters.
11. Karasu touching Kurama's hair and saying he should take better care of it.
12. In the fight between Karasu and Kurama, Youko told Juri not to move if she doesn't want to become plant food...but she moved and then literally froze after the plant "sniffed" her.
13. Juri leaving and saying she doesn't get paid enough.
That's what I can think of for now...