Why did every one like Mr. Bingley?

Mr. Charles Bingley is just an all-around nice person. He "was good-looking and gentlemanlike; he had a pleasant countenance, and easy, unaffected manners." Mr. Bingley is charming without being smarmy, like Mr. George Wickham, and rich without being snobby, like his very good friend Mr. Fitzwilliam Darcy. He is easy to talk to, desirous of pleasing others, and—especially in comparison to the rest of the Netherfield party—is absolutely without airs. His sisters and brother-in-law are incredibly unpleasant, and he contrasts totally with them. He is inclined to see the good in those around him, rather than the bad. Moreover,

he was lively and unreserved, danced every dance, was angry that the ball closed so early, and talked of giving one himself at Netherfield.

Doing something like dancing every dance shows Mr. Bingley's courtesy and his desire to make himself agreeable to his new neighbors. He has a pleasing personality and even plans to give a ball himself—something sure to win people over.

People like Mr. Bingley because, unlike his friend Mr. Darcy, he is not arrogant and obnoxious. He doesn't act as if he is too good for the local people. In fact, he has a bright, cheerful, and optimistic disposition. He is the kind of person who is easy-going and generally pleased with life. He is delighted with the neighborhood. He thinks the girls are pretty, and he especially likes the lovely Miss Jane Bennet, who likes him in return. The word for him, in Austen's day, was "amiable."
For example, Bingley cheerfully encourages Darcy to dance at the assembly and points out Elizabeth as a possible partner. But while Mr. Bingley, who sees the cup as half full, thinks Elizabeth is pretty, Mr. Darcy says she isn't pretty enough to tempt him. Given a choice, it's not hard to see why Bingley is the more appealing character.