I agree with what people have said about characters and plot. If I don't care for a character, then it's hard for me to be interested in the story. However, in many cases I would put a heavier emphasis on personal preference when it comes to defining what makes a character or a plot 'interesting.' There are books that are very famous and widely loved that I found tedious, simply because there's something about the characters or the plot that I personally just don't find engaging, but not because they're bad.
A good example is Wuthering Heights; while I loved Jane Eyre, which I think was written by the author's sister and was from the same time period, I could barely pay attention, particularly toward the end. The reason wasn't that the characters weren't interesting, it was just that I couldn't respect the characters and so they weren't engaging to me. (So I couldn't care about them, what they were doing, or what their children were doing.) Brave New World is another one I'd just as soon skipped, and Romeo and Juliet wasn't my favorite of Shakespeare's plays.
But, even if I don't personally care for a book, I like to look for both it's weaknesses and strengths as objectively as I can, and see if I can take away something useful. Part of writing a meaningful review to a book, I think, is differentiating between quality and your own tastes and opinions, though that can be hard a lot of the time. X3
But, anyway, for my own preferences. I guess I find I tend to like books aimed at teens/tweens. There's two reasons for this; one, I can trust them to be a lot cleaner (books heavy on swearing and sex really turn me off, and I avoid them if at all possible—I read Brad Thor's Blacklist a while back, and there were aspects of the plot that were really fascinating, but overall, I sort of wish I hadn't picked it up), and two, I've found as I've gotten older that I'm really attracted to books that appear simple on the surface, but are actually far more complex when you dig a little deeper.
Animorphs and Harry Potter are both very good examples of this, and Artemis Fowl, too. They're books that kids can enjoy, but they also deal with quite complex themes behind the scenes, and sometimes don't even directly address those themes, which opens up topics for discussion and debate. Harry Potter in particular has the appearance on the surface of being a fun kid's series (especially at the beginning), but the characters are rich and complex and develop over time, and the plot is so intricately woven over the course of those seven books that many of the things that happened in books six and seven were foreshadowed as early as in books one and two. I just love how books that appear simple have such a capacity to surprise you.
On the romance question—when I get really into a particular pairing, that's all I'll pay attention to in a series, but strangely, for the most part, I'm not a big fan of romance in general. A romance has to be built up in particular way for me to be interested in it. There are quite a few types of romances I don't like (romances that involve a guy who's a player are one, where he who goes out with girls all the time but never takes any of them seriously, then ends up falling for a girl and is suddenly transformed—I feel like these kinds of stories are misleading, because real life almost never works that way—probably part of why Mansfield Park is one of my favorite books), but I often have a negative reaction to those romances where there is any initial attraction based on looks. (That is, when the main character, upon first meeting the love interest, is like, 'Wow, he's so good looking.' ...Which pretty much eliminates ninety percent of the romances out there, because that's probably the most realistic portrayal of most romances.) I tend to prefer romances where the relationship starts out entirely platonic, but an authentic friendship is built up over time, and then it slowly turns to romance.
But, I can still very much enjoy series where there is that initial attraction in the romance; rather, it's just that the romance won't be a part of the series I'm particularly interested in. (Twilight is a good example. I'm going to take the unpopular side and say that I really liked the series, and Bella is probably one of the only fictional characters I've ever really related to [chronic introvert who avoids social events like the plague, among other things], but the romance was the one element of the series I didn't really like. I like romances that build very slowly, and they just got together too quickly for me to have time to grow to like it. But I will give Stephanie Meyer some credit—though I don't like the Bella/Edward romance, there are aspects about the relationships in the books that I find interesting. For instance, one of Edward's main strengths is that he's willing to sacrifice his own interests in favor of those he cares about, but there are many points of the story where this strength becomes a serious flaw, and is one of the most problematic aspects of Bella and Edward's relationship. He becomes so obsessed with 'sacrificing himself' in favor of Bella's 'own good' that he acts incredibly selfishly, which is one of the central conflicts of the books. Often in the process of trying to protect her, Edward attempts to get Bella to violate her own conscience, and has no conception for how important her own integrity and loyalty to those she cares about are to her. (In fact, Jacob Black, the main romantic rival of the story, is actually shown to understand Bella better than Edward does at many points. That's another thing I always appreciate in romances, having an authentic rival, who could be something the main character might fall for, as opposed to some rich jerk who there would never in a million years ever be a possibility.)
I guess that's something else I like to see in books, where strengths are shown in certain contexts to actually become weaknesses. I like to see elements that seem to demonstrate a deeper understanding of the complexity of relationships, and go beyond the usual clichés. My favorite though is probably when what seems to be a cliché (friendship/family is important, lying is bad, etc.) are ultimately validated, but shown in a much more subtle and complex light.
Wow, this is actually a really hard question to answer. There's so much to say. XD (I just narrowed down to a couple of topics. To be honest, my reactions to books aren't always consistent, and there are some things I'm in the mood to see one day that a week later I'm put off by. But the above are some general thoughts I seem to have carried for an extended length of time.)
“After all, absolutely no one can help but suspect a criminal, liar, and manipulator of committing crimes, lying, and manipulating. And of course, no one is more aware of that simple fact than Artemis Fowl.”
Opal sets into motion her most diabolical scheme yet, to frame Artemis and turn his closest friends against him. Only this time she has a new calculating partner who knows Artemis better than he knows himself. [An Artemis Fowl fanfiction, set after The Atlantic Complex.] https://www.fanfiction.net/s/8336552/1/Noble-Heart
...Shameless self-advertising, guys! C;
(And if you're really bored: http://axxonu.deviantart.com/gallery/28912232/Artemis-Fowl
AF fanart. ;J)