I'm probably really weird for the ones I like. I don't usually watch a lot of "mecha" anime, because it's frankly... not very interesting. It reminds me too much of anime like Dragon Ball Z where you get overpowered characters who just become more overpowered as the show goes on and they get more powers and unlock more of their mech's abilities and nonsense as the plot demands. I've been finding that what I like most about mecha anime is... when it is decidedly NOT mech anime.
So, here's my list and short reasons why in no particular order:
Code Geass - I like cerebral anime that revolve more around the intelligence of the pilots and experience of them instead of whatever fancy smancy crap they've got bolted to the frame. Anytime an anime with mechs turns into what is essentially a chess game or a batman gambit, I'm on board.
Aldnoah Zero - Same reason as above. Especially since our pilot is the underdog is every single way possible and imaginable and only wins because he knows what he's doing and outthinks the stronger opponents who have never had a single challenge in their entire careers.
Heavy Object - Not giant people robots, but giant tank robot things with strengths and weaknesses and specialities. The entire anime hinges on the premise that these mechs can ONLY be damaged or destroyed BY OTHER MECHS. As in, they are so overpowered that any standard military force is a moot point and only serves to essentially guard the maintenance facilities of these giant freakin' death machines called "Objects". What I like about this is... Two infantrymen who joined the military for decidedly non-military reasons... Manage to destroy one of these Objects BY THEMSELVES. Which sets them off on increasingly difficult and more deadly missions to take out even more of these Objects in other parts of the world using only minor explosives, their quick wits, and their absolutely crazy amount of bravery and cowardice. It's a fun ride and I wish there had been more.
MS08th Team - One of two Gundam series I like. This one I like because it's a love story on the battlefield... between two pilots on opposite sides of the war. I don't watch this for the mech fighting (because it's frankly freakin' dull). The characters and the love story are why I watch this one.
Iron Blooded Orphans - I watch this for the reasons I watch Code Geass and Aldnoah Zero. It's a bunch of kids who are underdogs who out-think their enemies most of the time. I don't care about the political nonsense or the uber-powers of the mechs.
Broken Blade - It's an anime about a guy without any real talent for magic or controlling mechs or whatever... And they manage to find a really super old mech that he can now somehow control. Oh, there's also an unrequited love story going on between the guy and the Queen of the nation. I liked it, it was interesting, despite how short it was.
Argevollen - An anime about an experimental mech and its mysterious origins... as well as about a super conglomerate of merchant guilds who create and run wars for profiteering. There's a love story in there too, which is slightly interesting, but the political intrigue and the mystery behind the mech itself are what made it interesting to me. Especially when the single mech starts turning the tide of war over the course of several months as the pilot learns how to fight in it and how to use it to its full potential.
Gargantia - I liked the concept of a stranded pilot finding himself as a "fish out of water", with no enemy to fight and no clue what to do with his life. The plot is "okay", but the characters are why I kept watching it. Also, the mystery of how and why ships that are like 1000 years old haven't rusted into dust yet was interesting to me. It's also never answered.
Arpeggio of Blue Steel - The mechs in this anime are actually ships... With female avatars. That transform. And are possibly from outerspace. A kid manages to acquire one of these ships... which is a submarine. He spend the anime being the only one able to fight back against the other ships who have blockaded all trade and all waters everywhere... and even prevent going into space with their superior weaponry. The world they built as well as the really cool tactics the kid and his crew of other kids pull off is why I enjoyed this one a lot.
Knights of Sidonia - I didn't watch much of the second season of this because it really wasn't as interesting as the first season... But the world that had been created in this anime was very interesting to me. Especially with the enemy they fight and this weird "pure human" they find as a candidate for piloting a really old mech they've got. While nearly everyone else is now part plant and can use photosynthesis to obtain energy and food... dude has got to eat... a lot. Anyway, the world of this ship and the space fights was really interesting to me and I stuck with it to learn more about it all.
Undefeated Bahamut Chronicle - I got into this anime because all the mechs had like "classes" and only the most powerful families had access to the "Legendary" ones. The world also feels very RPG and MMO-ish, so I liked that too. The main character uses two mechs... one is one of the most powerful mechs ever... The other is a "training" mech, which he tries to use for everything. In any case, he doesn't win any fight... but he doesn't lose either. He fights hard enough to bring every single fight to a draw. Unless something like lives are on the line and it isn't a competition... then the ultimate mech comes out. But, he doesn't want people to know he's got it or uses it, because it's the mech that was used to overthrow the last kingdom and send all the ruling families into exile. I liked it for the politics and the world. His "I always fight to a draw" was really cool too, especially since many of the powers the most powerful families have in their mechs are... well... let's just say a cheat code in a video game doesn't really do them justice for what they can do.
Cross Ange: Rondo of Angels And Dragons - This is a cheesecake anime. Through and through. But, I was enraptured with the world and how the people "who don't possess mana" are treated (namely like criminals... even if they're less than 1 year old... sent to a prison island!). I had a lot of fun with the anime and binge watched it over the course of two days. I even thought the ending was pretty good. The mech fighting is mostly just a confusing jumbled mess... but you're not watching it for that anyway. It's just mechs that shoot dragons to death. Sounds cool, doesn't usually look cool. The bigger storyline behind the people who can't use mana is much more interesting.
FLCL - It's got mechs in it. Much of the combat is between mechanoid type things. I'm counting it on that list. It's one of my favorite animes. Hard to explain why. Maybe I just love all the subtext.
Outlaw Star - Not sure if you could count this as a mech anime either... I do, 'cause of the ship and it's grapple arms. And since like half the anime revolves around those fights, or using the ship in that way. Plus, the cockpit layout reminds me of the Megazord from Power Rangers. So, it's a mech anime to me. I love it because the story is really good in my opinion. I also love all the characters. Plus, it makes me laugh.
EDIT: I forgot Eureka 7! An anime I watched solely for the love story and the "spreading mercy across the battlefield" stuff the main character finally decided on, instead of wanton destruction. The plot gets weird towards the end, but I enjoyed it.
---
And that's all the anime I can remember off the top of my head that are "mech", that I enjoyed a lot.
