Yes, I definitely think that these types of friendships do exist.
Friendship between Monica and Rachel- Two different people who have a lot of differences but still complete each other in every possible way. The way they understand each other and always come back to each other and love each other, I feel like I am with my best friend. The fights, yet the make-up, the fun of being together, etc. are very realistic and would make some sense if someone were a best friend.
Phoebe fits in perfectly with them. In every group of friends there's a weird person who's a little weird with crazy thoughts, yet you just can't live without that person.
As far as Ross is concerned, the bond he shares with his sister is admirable. It clearly shows how brothers and sisters are. They fight, they have family issues but still they love each other. She and Chandler are typical college friends who have known each other for a long time.
But the best friendship, of course, is none other than that portrayed by Joey and Chandler. It is much more than a friendship shared by two roommates. It signifies the best kind of friendship that can be between any two men. There are friends who hang around like this. It's the kind of friendship they can't live without.
Also, I think what was so well acknowledged on the show was how friendship attacked us and felt genuine in itself. The actors themselves had that chemistry.