When I think about it, Voltron was the first mecha anime that I saw. I liked it for having mecha, but something didn't quite pull me in. Then, Robotech came along and I was pretty hooked. However, Gundam Wing showed up years later and while not originally hooked, it grew on me until I am where I am today.
I couldn't exactly tell the "first" because I remember they were shown at about the same time when I was a kid. Anyway The earliest I could remember were: Transformers, Voltron, Voltes V, Daimos, and Macron 1. Among these, Voltron was the one that left my mind embedded with its narrator's voice saying: "From days of long ago, from uncharted regions of the universe..." XD
Now that I think about it, I think Diamos was technically my first, but I never paid attention to it really so it doesn't count. Voltes V was around the same time as Gundam Wing, back in 1999...
The first Macross, back when I was a kid in 1998 or so. A rerun, obviously, but still. After that, some show in 2005 that I don't remember, but it had something to do with mechs that wore capes and looked like knights. Don't remember much about that one. Then Neon Genesis Evangelion in 2008 when I finally got into anime.
My first mecha show? That would have to be Transformers in the early 90s, followed by the various Gundam series. Y'know what? I wish there were a Gundam series airing, and not one from the shitty 00 universe. That shit was so stupid, especially that wretched movie!
G1 Transformers (which I have the movie of, VHS tape, where Optimus dies)
Some Gundam Wing on Toonami
Neon Genesis Evangelion (props to all who love to do the Gendo Pose)