King of Braves GaoGaiGar andGaoGaiGar FINAL
The fight of a boy and his orange-haired cyborg best friend with a robot lion. The first is a series, second a sequel OVA. The series is very Monster of the Week-ish, but it's really fun. With courage, anything is possible.
GaoGaiGar -first opening

Aim for the Top! Gunbuster
Hotblooded lesbians and the only series I've EVER seen that has a realistic representation of travel near the speed of light. My god this ending. This ENDING. Also the first series ever produced by Gainax.
Gunbuster OP

Aim for the Top! 2 Diebuster
Same universe as Gunbuster. More hotblooded lesbians and this time with an absolutely adorable protagonist. Nono is love. Gainax modern animation craziness is in full swing (though toned down from FLCL), and once again, this ENDING.
Aim for the Top 2! Diebuster Opening

Shin Mazinger Z Shougeki Z Hen
Welcome to Mazinger Z, the first pilotable robot series ever created. This time around, there's a lot less monster of the week, and a lot more plot akin to a classical Greek hero tale. Kouji Kabuto, the grandson of the genius inventor Juzo Kabuto, becomes the pilot of the mighty Fortress of Iron, Mazinger Z. With this newfound power, Kouji has the power to become either a God or a Demon. The first episode is a half hour of wat, but it's good.
Shin Mazinger Z Shougeki ! Z Hen 1st Opening Edit MAD

Shin Getter Robo Armageddon
Oh my god, where to begin. Okay. This is a series that might as well be about three serial rapists who have been given three jets that can combine into a super robot with three forms. Ryouma Nagare is fucking insane and awesome for it. Getter Energy is pretty much where Spiral Power power came from. It does the same thing, and it's also green. I really don't know what to say about it. Mostly, it's hard to understand, but I'll be damned if it isn't fun to watch. Getter Robo was also the first combining robot, way back in the seventies.
Getter Robo Armageddon OP

Kotetsushin Jeeg
More Monster of the Week, but pretty good. Kenji gets dragged into a battle from two generations ago, and given a bike that turns into the head of a robot that combines with the use of electromagnetic... things. Pretty okay, episodic like whoa, but once things get going, it gets kinda crazy and awesome.
Kotetsushin Jeeg OP

Gaiking: Legend of Daiku Maryu
If you can stand some kinda sub-par animation quality and more Monster of the Week, it's pretty okay. I've never finished this one, but that's mainly due to time.
gaiking op2

And that's everything I'd mention for someone newish to super robots. A lot of them are Monster of the Week-ish, but seriously nice. Start with GaoGaiGar. It has a hefty episode list but trust me, FINAL is worth the payoff.

Also try Gundam X. Garrod Ran is my absolute favorite Gundam protagonist outside of Domon Kasshu.