Is it normal for girls to have a crush on each other?

Depends on the age and social/cultural context, I think.

(I am answering this as a heterosexual 24 year-old female)

It's not unusual for teenage girls to have crushes on all sorts of people. Particularly older persons -- most of the time it's someone you admire greatly, who seems superior in some respects, or beautiful. It's a lot like having crushes on teachers (remember the "oh, he's so smart/good-looking, when he looked at me in class the other day I thought I was going to faint!"), or on older males/females. Some girls have crushes on pop stars (who are intangible), and some on people that they see everyday (such as friends, distant relatives and so on).

What you asked would be particularly frequent in all-girls boarding schools (in ancient times :D), where younger pupils would nearly venerate the most popular girl or the most whateverteacher. There were even certain nicknames made for the girls who worshiped another student. :p

Also, if you have a best friend for a long time, it may be possible to start wondering if your feelings are more than just friendship. Because the feelings involved are so closely related: you think her pretty, smart, funny, you want to spend a lot of time with her, perhaps you hold hands when you're walking on the street... these all sound like a bit of a relationship, eh? Don't worry, they're not the same, even if they look alike. There is a line between the love of a friend and sexual love and you can cross it or not.