It's not required that a character be likable--sometimes we want them to be hated, but not always. Authors often discuss what makes a character likable, or even just worthy of sympathy.
Here's my list.
The character possess some trait or goal that is admirable. She has a noble goal or an inspiring quality. She does things we can respect and aspire to. It can even be simple: a man wants to provide for his family. A mother wants to comfort a child from the horrors of the outside world. Consider how much more those appeal than a man who just wants loads of cash and power.
The familiar character is one we can identify with. She wants something we want. She does things the way we would do them. She thinks in a way we recognize. In literature, the familiar provides validation. This is why the everyday hero is so popular in literature. He's one of us.
If a young boy tries to avoid the school bully, we can understand his actions because we've all faced bullies of some kind of another. We may not identify with a knight fighting a dragon, but when the village sweetheart makes him stammer and sweat, we feel like we understand. (And we might have even admired his bravery in that fight.)
We can just call this drama for short, but some personal definition is required here. By drama, I mean the character suffers and struggles. Something is wrong, something has been taken away, something awful has befallen our character--that alone inspires sympathy, a necessary ingredient, but that alone can fall flat unless the character gets up and does something about it. She tries to find balance, contentment and happiness again. If a man is abducted by slavers, we feel bad for him, but if he never fights for his freedom, how much of a story do we have?
(The struggle part could easily be slipped into the "admirable" category, and I considered that for some time, but I personally felt it is important enough to stand apart with suffering in the drama category.)
Writer of speculative fiction. Current work in progress is an untitled dark fantasy novella.