For starters, dragons are my favorite mythical creature (and so also my favorite Pokemon type). I find them to be interesting; they appear in multiple cultures with varying (and usually cool looking) appearances and meanings. In some cultures they represent power and wisdom, while in others they represent evil. Visually speaking, I've always like the appearance of black dragons more than any other dragon color. And Zekrom is black, so...
More specifically about Zekrom itself, I love it partly because of its role in Black/White. Black and White had the best story of any Pokemon game, imo, and the fact that Zekrom is a major part of that story just makes me like it even more. What I also like about it is what it represents on a broad scale: the duality of all things. The whole Yin/Yang, truth vs ideals thing that Zekrom and Reshiram have going. It's a fascinating concept to me, that seemingly opposing things are actually part of a greater whole, and both need the other in order to exist. It even jives a bit with part of my world view that things are almost never Black and White (derp, see what I did there?), but are usually a mix of both things. That's often how things are in reality.
Seriously, how many Pokemon represent something so deep sounding?
Zekrom is also great for battle. So is Reshiram, but what Zekrom has over it is the fact that it is one of the very few physical Electric attackers in the game (Electric is my 4th favorite type, btw). The vast majority of Electric types are specially based, so its easy to counter them in general with special walls. Not the case with Zekrom though. And while it misses out on being neutral to Fairy like Reshiram, its one of the only Pokemon in Ubers to resist Flying, and can easily threaten titans like Lugia, Ho-oh, and Kyogre with the strongest Electric attack in the game, STAB Bolt Strike. Hell, Bolt Strike 2HKOs the majority of the Pokemon in the Uber tier. It does suck that both its STABs have Pokemon with immunities to it, and its movepool is a bit lacking, by hey, you can't get everything.
I also don't hate Reshiram; I like it quite a bit too (and Kyurem, I like it as well). Sometimes I get the feeling that people assume I dislike the rest of the Tao Trio because Zekrom's my favorite.