Well, the first anime I watched to completion, in my current cycle, (For some reason, I tend to go on these weird cycles of stuff) Would actually be, and I'm kind of embarrassed to admit this, but, um...
To Love Ru.
Yeah, you heard me.
I immediately followed it up with Neon Genesis Evangelion, so, it's cool.
Edit:
Actually, the very first anime I can remember watching, waaaaaaay back in the day, when I was but a young lad, would still be Neon Genesis Evangelion. But I didn't understand any of it, and it gave me nightmares for weeks.