Shin Getter Robo

Getter Robo is by far the biggest influence on TTGL, as admitted by the staff and as evident in the show. New Getter Robo isn't the best of its franchise (the Getter Robo Saga manga is), but is likely the most solid and accessible of the animated incarnations. 

Both ovas are by Dynamic Pro and they share the same director. If you just want gore + mecha, look no further. 

Both are modernization "alternate timelines" of souped up versions of classic Super Robots. Mazinkaiser is the more modern and beautifully rendered series while Shin Getter Robo has a grittier artwork and pacing that I prefer so even though this is a recommendation section, I would suggest not taking the similarities much to heart. Treat this more like two similar series but one having more flash and the other having more substance. Shin has the substance, Mazinkaiser has the flash. ...but don't forget...these are still remakes/sequels of classic Super Robot series with depths that may disappoint more modern anime fans so make the flash and substance issues relative to how those classic Super Robot series were and not a general list of modern mature anime in general. read more 

demon-like species from another dimension attack the earth. the humanity's only hope is a set of giant machines that can combine into a humanoid robot, piloted by a hot headed team of specially selected young people. the robot appears to not be just a regular mechanism, but mysteriously responds to pilot's will. 

They are 2000s reboots with retro art styles based on classic super robots series written by Go Nagai, aiming to be closer to the manga than their original 70s version. Both are filled with action, violence, JAM Project music and all the insanity one expects from Dynamic robots. 

Gunbuster is the more depthful series by a mile but both have parallels of a bright mecha future turned dark and then turned bright again. (Not in lighting but in optimism/pessimism levels) Compared to most recommendations though, watching one or the other will tone down your liking for the other series because of the quality of the events. Because of this I recommend watching Gunbuster first as Shin Getter Robo is the more forgiveable series to hate. (Forgiveable as in even if you don't like the series because it doesn't meet the standards set by the previous series, you could still gleam enough enjoyment from it because of the addition of an iconic Super Robot series) read more 

Like Shin Getter Robo vs Neo Getter Robo, this is another continuity reboot of Getter Robo. This time it sticks closer to the original manga.  

Gurren Lagann takes direct inspiration from the Getter Robo saga, the similarities are uncanny, down right to the color scheme of the mechs. The stories are similar about humanity struggling to survive a post-apocalyptic world and the characters like Ryoma Nagare and Hayato Jin were a big inspiration for Rossiu and Simon/Kamina. Shin Getter Robo is a must see for any Gurren Lagann fan 

Both are Super Robot shows with super manly protagonists and ridiculously awesome stuff happening all the time. It doesn't get much more over the top and hotblooded than either of these series. 

Remake/tribute to another Go Nagai favorite, that's a bit more faithful to the manga. Expect lots of violent rape.