Dragon Ball, One Piece, Bleach, and Naruto all have blood. Why doesn't Fairy Tail have it?
The reason for this is censorship. Fairy Tail has a 'PG-13' age rating; most shows with this rating do not show gore.
Another example of something they censored would be that in the manga, Gray Fullbuster is a smoker. They took this out in the anime because they were afraid it might influence children to think that smoking is cool.
This can be seen in Chapter 4, Page 20 and Chapter 10, Page 6-7.
On a side note, the first OVA ("Welcome To Fairy Hills!") is the only episode I know of that shows blood before Fairy Tail 2014.
Levy after Erza smashed her face into the wall (10:05).