First of all, make them relatable. Their problems need to feel plausible, something the reader can identify with. Even if you're writing epic fantasy, people aren't different. They can still have problems living up to a parent's expectations or have relationship problems. If your main character is a supermodel who also sells best-selling mysteries and she's flying off to Hawaii to get over her breakup with her movie-star boyfriend...we aren't going to care about her problems.
Make them suffer unjustly. If someone starts playing tag with cars in traffic and they get hit, we're not going to feel too bad for them. Likewise, if someone decides to ignore warning about a haunted house, that cuts down on our sympathy for them once the killer starts warming up. Ideally, your character should suffer and suffer badly but if they aren't to blame, we will side with them as a reader.
Make them care about someone else. Another way to build sympathy is to have your main character help the helpless or show concern for others. If your protagonist is a unstoppable killing machine, that can be fun for a while but we won't really care about them any more than we care about losing a 'guy' in a video game. Have your protagonist care about something other than themselves or their plot goal.
Make your main character 'cool'. Have them say all the things you've always wanted to say. Give them all the good lines. Have them smart off to authority figures. They may not (and probably should not) get away with all the time but have them get in people's faces. Have them dress well. Show them in control of circumstances that most people get wrapped up in.
Make them competent. A main character that can fix a car, parachute out of an airplane, win a fist fight and cook dinner will draw our admiration. If they fumble with their keys or can't protect themselves or botch giving first aid, we grow frustrated with them. That doesn't mean writing flawless characters. But whatever your character 'does', make sure they can do it well.
Make them have a sense of humor. Humor, especially in the face of despair, makes us identify with your protagonist. I'm not saying they should be flippant or light-hearted when it's not appropriate but a person who can laugh at themselves draws our admiration.
There's more, I'm sure. Let me know what you think makes for a likeable character.