As some others have said, I don't try to make my characters likable so much as understandable. I think sympathy is almost automatic once you have a true understanding of how the character thinks and why they act the way they do (assuming all these thoughts and reasons make sense in some way). Some of my characters do very bad things (steal, murder in cold blood, even rape) and never repent. If I've left my readers doubting that this makes them bad people, then I've done my job.
I've never written about a 'normal' person, and doubt I ever will. It seems like a lot of books feature the 'normal everyday person suddenly finds self in exceptional/dangerous/exciting situation' kind of character. Frankly, those characters almost always bore me. Sure, they're realistic, but reality is boring. If I want reality, I'll live my real life. In a book I want things bigger, better, and larger than life. So that's how I do my characters. Now my characters are NOT unrealistic. In fact, they all have a basis in real psychology and people I've met in real life or read about in (non-fiction) books and articles. But they certainly aren't 'normal everyday people'. In my fantasy books they're elite pirates, thieves, assassins, and spies, and in my contemporary they're serial killers. They're extreme characters, forged by extreme expierences, who take extreme action. The part of writing I enjoy most is taking all these extremes down to a level 'normal everyday readers' can understand, and even relate to. Most of us will never be in situations as intense as those I write about (myself included), but we've all felt things like anger, love, hope, desperation, fear, and loss. I think most readers are imaginative enough to take these basics, and imagine what the character must be feeling. If the writing is good enough and the character is well-developed enough, I think anyone can relate to anyone.
Oh, and humor. Humor goes a long ways towards making readers like characters.