I was thinking about stuff I should write on this site. You guys are quite lucky, there is lots of stuff (a tribute to my crush, a romance story, and an excerpt from my drama novel among them) that you will all get to read and hopefully enjoy. But for now, I want to do a "fictional" bit based on the issue explored in "Fourteen Seconds" (my only work on this site). My problem is getting the reader emotionally invested in my character. She's likable enough and the plot is decent. But I want this to be good. I want this to be better than good. I want YOU to remember it. So, how do I do that?
Who are the characters you fell in love with (as interesting and likeable, not necessarily romantic love)? Harry Potter is a classic. He's picked on, but stays nice; he has chances to be self serving, but he sacrifices wins when he thinks others are in danger. Katness Everdeen in the Hunger Games is another one who acts to help other people in spite of putting herself in danger. People like the character who is very clever, like Poirot, Sherlock Holmes, James Bond and MacGyver, maybe not all characters you are familiar with.
For me a likeable character doesn't necessarily have to be faster, smarter or stronger than everyone else. One thing I noticed is that Orphans, for good reasons, are quite popular. At least in Western Society (pardon me the generalizing term) "we" almost automatically feel attached to these social outcasts. I think there are several things about orphan characters that make us relate to them so easily. First and foremost (feel free to hate me for saying this), people like to make their own problems bigger than they are. Having these (orphan) characters to which terrible things happen is a way to shift our problems into the realm of fiction. "We" seem to be quite good at this form of self-wallowing, where suddenly, because we feel so connected to the character, his/her problems, and the scope of those problems, transfer over into our own world. Secondly, orphan characters are often likeable because the internal struggles we all go through at one stage or another, are much more pronounced and vocalized with them. Whereas "normal" people will often keep such struggles contained, orphans -due to them being orphaned- vocalize these struggles much more. I read a whole file on the subject once, i'll see if I can find and attach it for you: https://www.ideals.illinois.edu/bitstream/handle/2142/8216/librarytrendsv47i3p_opt.pdf I am not saying you should make your character an orphan, my point is simply that there seem to be several things about orphans in particular that makes the reader favour him/her as a character and establish a quick connection. Your challenge will be to apply those character attributes to a non-orphan character, if that's what your MC is.
Make us care about her problems. Make us sympathize with her. I believe having an emotional connection with the character (or a group of characters) is far more important than having readers like her. To use an example from TV, the show Breaking Bad has a main character who has done some bad things, but I still sympathize with him because I can understand where he's coming from. And that I think is the key to making readers remember a character.
I think another thing that would help is giving the character a few specific things to remember them by, but not physical tags, like Harry Potter's scar or something. Characters can be defined by memorable actions that exemplify their personality and idiosyncrasies, like how they reacted in a certain situation. What stood out for me was in Cat's Cradle when Felix Hoenikker tipped his wife for a meal. That, and other anecdotes made him more memorable for me despite never meeting him, which was important as in the novel he was dead to start with. And of course never to tell the reader through another character's mouth a character's personality or traits. As for emotional investment, I like self-aware characters that grow and evolve and learn from their mistakes. I'd be much more connected to a character if they continued to change and surprise me in what they do, say, or think.
Harry Morgan, the m/c in To Have and Have Not, is not at all likeable, and yet his situation makes you hope he comes out of it all right. Sometimes, it is the circumstances of the character, not just the character's traits, that draw you in and make you root for them. And then there is someone like Earnest Pickering in Major Pickering's Last Stand, whose initial problem is one that will likely make most readers shrug, and as he persists, might make you cringe. And yet, as he grows through circumstances, his basic character dictates that his priorities adjust, drawing the reader in.
Thinking back to characters I've liked, they're usually honest, even about their shortcomings. They usually end up in embarrassing situations, especially when they're trying too hard. They don't whine, but when they face an obstacle, they do their damnest to overcome it. They also tend to be quite average, no particular superpowers or stunning looks, perhaps that way they're more reletable which makes them more likable? I'm not sure, could be just me, 'cause many readers also like the escapism factor in characters. One of my pet peeves is some stunning rich guy falling for a mousy girl. Yeah, like, if there's no one else around then sure, but the sad fact of life is that gorgeous people mate with gorgeous people, average with average, etc. Or maybe it's just in my immediate circle of friends, so don't take my cynicism at face-value. There're always always always exceptions, but when the exception becomes a best-seller norm... meh. I guess this is how I invest emotionally in the main character, usually.
I am going to agree with @KaTrian here. The character has to be honest, and the less "whining" the better in my opinion. I cannot stand to read a main character who is whiny. Also, someone who is humble helps me as well.