Pretty much agree with the suggestions. The Brave series is a really good place to start with super robots. Besides Gaogaigar and Might Gaine, you can also watch Fighbird. The fansub has recently been finished. I'm not certain, but I believe they're working on Dagarn now.
The Getter Robo OVAs are probably the single best adult super robot anime. They're extremely violent, though. So if you're not too keen with seeing blood, then you may not like it.
Mazinkaiser is a good series. It's a direct sequel to Mazinger Z and Great Mazinger, but it's not really necissary to have seen them to get what's going on.
Koutetsushin Jeeg is really good. It too, is a sequel to an old series, but you get some flashback stuff to give you an idea as to what came before.
Gaiking: The Legend of Daiku Maryu is a pretty good show. It's mainly a show for kids, but it keeps itself enjoyable for the older fans.
Overman King Gainer has the best opening ever. It's not a spectacular series, but it's an all around good show. It has one of the oddest finales, though.
Gear Fighter Dendoh is a pretty good show. Sunrise used some concepts from the canceled Brave series Baan Gaan in Dendoh. It's a nice solid robot show for kids.
Aquarion is a pretty good show. I was a little disapointed with the ending, mainly due to certain characters pretty much being forgotten, but still a good show.
Gunbuster and Diebuster are amazing shows.
It's not Japanese, but Megas XLR is just as much of a super as anything else that's been mentioned.