Once I got over that weird fear of being judged for being a sissy for it (even when no one else was around), I started doing the honest thing and selecting the character I was most interested in, which is the female character 70% of the time. Blaze in Streets of Rage, Tyris in Golden Axe, Honey in Fighting Vipers, Felicia in Vampire Savior, Selena in Guardian Heroes, Tillis in Burning Rangers, Beltiana in Batsugun, Edie in Elevator Action Returns, Rouge and Ayane in Power Stone, et cetera. It always helped that Sega games sort of have a proud history of respectable female leads: Alis, Arsha, Janet, Ulala, Aika, Gum, Hibana, Orta -- this goes all the way back to Ninja Princess, I suppose. Or, actually, I forgot about this, but the biker in Hang-On!
http://www.hardcoregaming101.net/hangon/racinghero-ending.pngThat made me happy to find out, since I've been a Hang-On addict since 1995.
Anyway, I'm like Randroid to a certain extent -- if I'm building a character from scratch, I'll make it look like myself. If I'm playing a game that's mostly stat- or technique-based I'll choose the character that best suits my play-style (I love Pai's design and backstory, for instance, but when I'm playing Virtua Fighter Lion is almost always my best bet) -- it's only if I really love a character design (like Blaze, for instance) that I'll work with their flaws out of a desire to see that character succeed, but admittedly if I'm in it for the story or to root for a character arbitrarily I tend to gravitate toward female characters.
What really bothers me is the abundance of hentai for every respectable female character, though. The pictures I've seen of Blaze, Honey, Ulala, and Aika in particular really sting right in the childhood. Not that it wasn't 100% predictable for all of those characters... except Aika. That's just wrong.