What you currently use?
Firefox
What exactly do you want in your browser
I want something that I can, like Jari, add extensions to. I want one that allows someone who is HTML literate but hasn't made a webpage for years to be able to view source code to see somethnig specific. I want a browser with an efficient download manager and I want the ability to pause downloads when I wish. Sometimes between classes I find myself unable to complete a download; I don't want to have to close up shop, go to a classroom that has the internet disabled by proxy, and have to begin my download all over again. I also want a browser that allows me to hit up any popular search engine with great ease. The ability to search any search engine within the browser, without navigating to a new page is sheer brilliance, IMO (and the Google Toolbar for IE attempts to emulate that). I can search Wikipedia, Uncyclepedia, Google, Altavista (why, I don't know, but I can), Torrentspy, Yahoo!, E-Bay, etcetera, all with very little hassle.
In short, I want a browser that comes out of the box, so to speak, extremely versatile, that can be made even more versatile by downloading and installing a few plugins (right now I have one that allows me to see what the weather is like on campus, so for those few short minutes before I head off to class I can see what shitstorm I'm running into).
What makes your browser better
IE is all cluttered up, IMO. Firefox seems more down-to-earth, and it would appear that a lot less space is wasted on bars and so forth, with the majority dedicated to content, which is what I'm paying x amount of dollars a month to see.
What do you love the most about your browser
Just it's versatility, in short. I have the feeling that I can do anything with my browser. It's more secure than IE, etcetera, but the other main point is that Firefox can do essentially everything that IE can do, but IE can't do everything that Firefox can do, which is the main problem. Firefox is like IE +1.
What would make your browser better
Beats me.