In which anime characters fight using top-toy like objects?
Sounds like you are talking about beyblade.

From Wikipdia:


  Beyblade, known in Japan as Explosive Shoot Beyblade (爆転シュートベイブレード Bakuten Shūto Beiburēdo?), is a Japanese manga series written and illustrated by Takao Aoki in order to promote sales of spinning tops called "Beyblades"


(emphasis mine)

Here is a picture of one of the main characters holding a beyblade (taken from fanpop):