Alexander is one of my favorite leaders to play, if not my #1 favorite. The boost that he gets to great people helps out a lot throughout the whole game, and the aggressive characteristic is nice to have. His UU, the Phalanx, I have used to defend my cities (well, not uniquely, but in part) against Knights, and after promotions, even against Russian Cossacks. (with pretty good odds, I might add, considering its strength and hammer cost, I might add!)
In terms of an overall strategy, I typically expand enough where it's likely that I'll obtain Iorn or Copper early, and then build a city defensive core of about 60-70% phalanxes. I also promote one in each city with City Attack, should the need arise to expand via force. Alexander's quite useful for doing that. I have been in four wars with Roosevelt in my current game, razing 4 of his cities, taking 2, leaving him 2 (1 which will soon be mine via culture.. i have it practically surrounded).
Great Scientists are very helpful in obtaining military techs. Religiously, find out what's popular halfway around the world and make sure you can be friendly with them. Trade them military techs for others, even if it means getting a little bit of a ripoff out of the deal. (Ie, send 60 extra gold for a tech to obtain a tech of the same Erlenmeyer Beaker value). (Oh my God, I'm such a nerd for calling them Erlenmeyer Beakers).
Lastly, keep spies in the surrounding territory. Even a few turns warning in advance is a big help to Alex. I found this necessary the hard way when one of my opponents (well, Russia) built up 18 Cossacks to attack my 5-rifleman/3-grenadier/3-phalanx-defended city. And she was coming from halfway across the World, working across a pangaea. Psychotic bbbbii..erm, leader. I couldn't tell you for sure, but I think the AI might realize that an aggressive leader might be tougher to take down through military might. I've never seen such a large stack (well, 2 stacks). Defending that was miserable, the aftermath as bad. I was left with a rifleman and a phalanx. (and slightly thinned out defenses in four other cities)
Mike