Back when I had Pokemon Yellow, I never nicknamed any of my Pokemon because -- feel free to laugh -- Ash didn't in the anime. The anime was the first major Pokemon thing I got into and because of it I thought that I somehow wasn't supposed to nickname my Pokemon. Thinking back on it, it was all hilariously misguided.
Moving forward, as I play Pokemon games, I definitely intend to nickname just about all of them, making possible exceptions mainly for Pokemon where the original name is really awesome or just Pokemon I don't care about at all. Most people who talk to me in casual settings like Skype chats or the shoutbox know that I'm all about nicknames. :bleh: But also I think the personalization element makes it really cool too. I dig making my Pokemon my own, collecting awesome monsters and giving them cool names and really giving them some significance and customization. I love any kind of customization element.