Both Hollywood and Bollywood have music/songs in them. You can clearly see songs in bollywood movies and you can check on end credits on hollywood movie about tracks they've used in it.
Why Bollywood movies often has dancing sequences and Hollywood movies rarely have them (almost never), is mainly because of cultural and geographical and historical reasons for both. In Bollywood, songs play important scenario in popularity of movie and income. Almost every movie has a in-movie song (clear segment dedicated for the song and song played almost full length). It's from long ago (since the beginning of bollywood movies) and it's like a tradition now. Viewers always expect musical performance in movie and songs play a important part in the movie. It can set or change mode of the movie, can be used to illustrate some emotions better culturally accepted way (love, friendship etc..) by using combination of music, rhythmical words and moving picture.
Sometimes songs in a movie become so popular it'd earn extra income. in Bollywood, viewers always looking for movie songs, in early trailers we can see they promote the movie with titular song(s). Being traditional item in bollywood movies, songs plays a important role. I can also add something about bollywood cinema, as a my opinion. Most of the movies in bollywood are based on love stories somehow. From the beginning bollywood used songs to illustrate love and affection for one another in main characters in the movie.
Using songs are traditional in bollywood cinema.
Almost everybody is using in their productions. Being a common item, viewers expect songs in a movie. So usually producers want to get better viewer attraction and bow down to common practice.
Songs being somewhat common in a movie, it gets part of movie's attention.Sometimes songs get more popular than the movie. Or sometimes songs will be popular but movie will be a failure. It'll be a somewhat good way to earn income from songs, rather than being a complete flop.
Turning to Hollywood, It doesn't get affected from cultural effects I mentioned above. Hollywood has more categories than Hollywood. and also in Hollywood they try to go for different story always possible. I'm not saying Bollywood always go for same story, but in Hollywood, movies has a wide range of varieties. category-wise, genre-wise and story-wise. Nevertheless Holywood uses music and songs in movies. But main difference is most of the movies doesn't include separate segment for the song/musical section like in Bollywood.
Being said that, Hollywood has some musical movies, sometimes actors sing and dance too. There are lot of them and you could find them in imdb on categories musical. Anyways I should mention the movie Sweeney Todd, starring Johnny Depp