I'm gonna start watching Hayate no Gotoku anime and I haven't read the manga so I need to know whether the anime adapted the manga closely. I am referring to all of the anime seasons and movies .
As nhahtdh pointed out, the first season has a lot of original content of the manga, but the time scale is completely different. Inside the anime, the first season was equivalent to more than a year, however in manga only 9 to 10 months have passed till then.
The second season completely sticks to the manga. So it does not seem like a continuation of first season.
The story of the movie: HnG Heaven is a place on Earth is not at all related to manga and so is the third season. However, the story of the third season was written by Hata Kenjirou (the Mangaka of HnG).
The new characters introduced in third season are present in manga, but the story is completely different. The fourth season HnG Cuties is a series of 12 episodes. The first 10 episodes are based on discrete chapters of manga. Each dedicated to some character(s). The last two episodes are not in manga.
Overall, you should give it a try!