Sooo... I'm gonna try and weigh in on this topic!
I have never been a mecha fanatic and have no interest in building model kits, etc... but I believe in keeping an open mind to just about anything when it comes to not just anime but animation generally and live-action film and television as well - I'm a lot more interested in the story/characters/acting/comedy/music/animation than whether it contains giant robots or not, and that's long been my stance. So some shows with giant robots (or things that are initially presented as giant robots then turn out to be something else!) that I have seen and enjoyed are:
Neon Genesis Evangelion (I have seen TV version, director's cuts of all TV episodes that have them, Death and Rebirth, End of Evangelion, and rebuild films 1-3 in their 1.11, 2.22 and can't remember which cut of the third one it is I saw.) - I don't really know how much I can add to discussion of this title at this point but I will say that I really empathise with Shinji a lot and can't stand it when people give him **** for being a teenager/boy with depression who doesn't always handle things very well. Really felt for the poor guy. I liked the female characters too though Asuka can be a complete b**** and Rei can be cold. I get they have their reasons for that too though. Honestly though, that said Evangelion really compounded my depression on first viewing and I didn't go back for quite a while after that (I was a teenager when I watched it and it messed with my head in ways I couldn't really deal with). That obviously means it had an impact, but that's not always a good thing depending on what that impact is. I still love it but yeah :/
Bokurano
Dai-Guard
(The Vision of) Escaflowne
Eureka Seven
FLCL (if it counts lol)
Gunbuster
Gunbuster 2/Diebuster
Gundam 0079 Movie Trilogy Version
Gundam 0080 War in the Pocket
Gurren Lagann (though I don't like it as much as some people here do - I much prefer Kill la Kill)
Patlabor movies (1 and 2 were best though 3 still has some things going for it)
Rahxephon
I honestly quite liked Gasaraki the only thing about it I found distasteful was the nationalism, and the ending was a bit rubbish but it was mostly enjoyable for me, I thought they incorporated traditional noh dancing/theatre/rituals(?) with the mecha really well
Series on my list of stuff to watch:
Armored Trooper Votoms
The Big O
Code Geass - I have actually watched the first season and some of the second, wanna finish it tho)
Darling in the Franxx
Dragon Pilot: Hisone and Masotan
Flag
Full Metal Panic (I have actually seen Seasons 1-3 but not 4 or 5, if I'm honest the first season was my fave of the ones I have seen but I liked some things about Fumoffu and Second Raid as well)
Gargantia on the Verdurous Planet (though I find it's portrayal of trans/crossdressing characters to be cruel and inaccurate, based on offensive stereotypes)
Ghost in the Shell (I wanna rewatch the first movie and SAC TV and movies cuz it's been sooo long I'd need to see what I think of it now and I'm not sure I ever finished the second season of SAC, I certainly didn't watch Solid State Society in full and would really like to)
Giant Robo: The Animation (OVA series)
Godannar (those hilarious ADV trailers sold me on it XD)
Gundam - some of the many series out there, but not all of them
(SDF) Macross, Do You Remember Love? and Macross Frontier
(SDC) Orguss (I think this had mechs? I remember enjoying what I saw of it)
Patlabor TV and OVAs (I have actually seen the first OVA series, I wasn't head over heels but it was years ago so I'm willing to give it another try)
Planet With (words cannot express how stoked I am to see this series)
SSSS. Gridman (tho again I don't think I'll like this as much as others did - I saw the first half or so and it was good but not the best)
I loved the Knights of Sidonia manga, wasn't as keen on the anime.
I'm also curious to know if anyone here is a fan of either Sym-Bionic Titan or Exo-Squad? Two US cartoons with a mecha element that I really enjoyed (though I haven't finished Exo-Squad yet but it's definitely something I will finish).
I will try and post deeper thoughts on some of these other titles in this thread at some point
Question: Is there a magical girl thread on AUKN forums? I'm no expert but might be a good idea for someone to make one