"Oh woe is me. Two perfect guys are in love with me because I'm just so darned nice. Why did this have to happen to me? It's just not fair!" 
                          
And the reader goes: "Oh sod off." 
                          
A further problem with very good (or almost perfect) characters: Frustrating the reader.
                          
When I sent The Vanished Knight out to critique partners the first time, ALL of them (and there were ten) were frustrated with Callan within the first five chapters that she featured in. The way I'd written her, she had a temper, (So no, not a Mary Sue) but she was scared of reacting to people pushing her buttons. So her temper would eventually explode inside, but she'd do nothing about it and people would push her around. And the readers hated it. They didn't like seeing her suffer for nothing and willingly -- with almost superhuman determination -- take all their crap. Beyond a certain point, they couldn't believe it either. There goes the connection to the character and suspension of disbelief. In a few short chapters. 
                          
The fix for this was actually really easy, but it made her story awesome. I'm not going to tell you too much, but let's just say that in those five chapters where readers got annoyed, I let her temper slip despite her best efforts. Not once, but three times. 
                          
And then I made the third scene, the one where she just couldn't stand by and do nothing, EPIC. 
                          
The same sort thing works for Mary Sues and Marty Stus. If you really do want people to like your character, make them less perfect. This means making them scared of stuff even if they're brave. Or capable of doing some very dark deeds even if they feel guilty as hell about it later. You know... stuff like that. Real weaknesses. Not something as stupid as insecurity when anyone with half an eye could see she has nothing to be insecure about.
                          
Imperfection creates something to relate to. Make sure your character has it. 
                          
But what then, of the opposite? The character's so bad that no one likes him/her. 
                          
Now hold on to your seats, ladies and gents, because my answer might just blow your minds. 
                          
A reader doesn't have to like a character. They need only relate to him/her. 
                          
In other words: I as reader don't have to like the character. In fact, I can be pretty sure that s/he's a brat/bastard/sociopath/you name it. They can do terrible things. Murder people, steal, beat people up for no reason, and on and on. But if you do the characterization right, it won't matter. I'll still want to see what happens in the end. And I might still grow to care about the character. 
                          
Basically, this comes back to motivation again. Motivation and the character's world view. If you let us readers see either of these or both, we'll go with what the character is doing for the sake of seeing how it all pans out. Give them soft spots and good characteristics, and I'll probably end up liking them despite myself. 
                          
In The Vanished Knight, I actually have two such main characters. One is James (who I'll focus on because the section I'm talking about is available for you to read). He is a brat. Totally. Completely. In fact, I didn't even like him when I started writing him. But as I wrote him, I started to understand what drives him. And basically, that was how his parents treat him. Even when they're not there, they still color his actions, and it takes him some time to figure out he's wrong. 
                          
However, because I showed that side of him (by having him react to his parents' callousness, even if readers don't know why they treat him like this), people could understand where the rage came from. As a result, some readers love him from the first. (Which I really find interesting.) In case you're wondering: I like him too, now. And he's becoming a better person as we go on. 
                          
But yeah. James is just a brat. However, you might know from watching t.v. that a writer can make his/her audience accept anything and still want the character to win. Even if he's, say, a serial killer. Look at Dexter. He's totally sociopathic. And if you read the books, you'll realize he really has very little true emotion to connect to. BUT. He has a code of honor, only hunting other killers. And he's protective of those closest to him. He's also got a wicked sense of humor. Right there, off the top of my head, I listed three things that made him relatable to people, and I haven't really even dug past the surface of what makes Dexter, Dexter. 
                          
I mean, only killing killers doesn't really diminish the fact that he kills. Nor does his protecting people in his inner circle. And his humor, well let's face it, is sort of depraved when it comes to the fact that he's really laughing about people he has killed or will kill. And yet, we like him, despite the fact that he's different, but because of the things we have in common. 
                          
That's all there really is to it. Once you've gotten the reader to relate to your character, the relationship grows out of "going through" things with the character. As long as you keep your information coming in at the right times and consistent, readers will automatically start building the relationship themselves. 
                          
Because that's the thing writers forget. When readers open a book, they want to be swept away. They want to care about the characters. Therefore, you the writer only need to create opportunities for the reader to connect, and it will happen. 
                          
So go on, show the different sides of your character. What makes them happy? Angry? Sad? Excited? By showing these things, you're connecting the reader more and more, and your book will be better for it. 
                          
Thanks for reading! If you want to check out The Vanished Knight, the whole book is now on Wattpad. Please do read it, if you like, and let me know what you think. 
                          
As usual, you're welcome to ask me questions about writing in the comments. If your question inspires me to write a new section, I'll dedicate it to you. 
                          
Coming up: 
                          
Showing vs Telling
                          
Narrators
                          
Worldbuilding (Dedicated to JaneCorinne)
                          
Internal Logic
                          
Ideas and Cliches