Anime

Monster Musume. It's far better than the premise would lead you to believe. Rachnera best girl, incidentally.

When I was in college, I had a tendency to grab random series from an fserv in IRC. One day I got Kaleidostar not knowing what it was and proceeded to marathon the whole 50 something episodes. I told the homies I was in my room watching porn lest they know I'd secretly become invested in binging anime made for middle school girls.

I think this depends on the intended audience. My answer would be different depending on if I am talking to somebody familiar with the anime landscape vs somebody not familiar with anime. Trying to keep things generally spoiler-free below...

For the anime-initiated

• Fullmetal Alchemist (not Brotherhood) - I know, this makes me a terrible person, but I actually like the anime-original ending of the first Fullmetal at a conceptual level. It raises a lot of questions about the nature of alchemy and how it is inseparable from violence. You can really read a lot into it and apply it to things irl.
• Usagi Drop - The manga has ruined this series for many, many folks in the greater anime community. However, just taking the anime as a standalone piece of media, Usagi Drop is a great series.

For casuals

• The 100 Girlfriends Who Really, Really, Really, Really, REALLY Love You - The title of this series makes people think that this is just some trashy, fan service filled, harem trash....which it kind of is. But, at the same time, it is actually hilarious and quite touching a lot of the time. The premise is ridiculous, but so is how much effort they put into making sure that it is executed to perfection.
• Reincarnated as a Vending Machine - Another series in which the title makes it sound incredibly stupid. However, I enjoyed this show a lot and it was way better than I had thought the premise would allow.
• Rascal Does Not Dream of Bunny Girl Senpai - This is a series that I have recommended to people irl before and gotten some weird looks in return after they hear the title. In reality, this is a great series that uses supernatural occurrences to explore the insecurities and difficulties that arise as children grow up.

Onimai: I’m now your sister

It got looked down on as it involves a man being transformed into a little girl and making friends at school with other girls that age. But if you ignore the fact the younger sister was a man it’s just a story about an elder sister helping her little sister get out and make friends.

• Miru Tights

I didn't have a thing for tights and stockings untill I saw Miru Tights. This anime made me appreciate stocking, tights and feet related stuffs after watching.

Fate/kaleid liner Prisma⭐Ilya. I swear I'm not a pedo. I just want Ilya to be happy.

All of them. I never talk about it in public, except giant robots. It's the only socially acceptable version. I thank Transformers for this.

Mushoku Tensei because of the worldbuilding

Hmmm.

I don't really have series I'm ashamed of liking. Perhaps one's I know are trash... I try not to be a weeb in the company of most people, in order to respect their disinterest, but I don't have anything that makes we wish I'd disappear if people found out.

I watched everything there was of Freezing, for the sole reason that HanaKana VAs a character that is thirsty as hell, which is somewhat embarrassing.

Sakura Trick or Seitokai Yakuindomo maybe. But I don't really talk about Anime with anyone so who cares ^^

Inukami!

It's constantly lewd, silly, and is simultaneously an example of a harem anime and making fun of perverts. The series has moments that will make you cry from laughing so hard, and times when you get a little emotional, and then you'll go "fuck yeah" as something cool happens. It sort of has the premise of 'taming' spirits and using them to battle bad spirits, but most of the time they end up fighting the over-aggressive nerd who gets a nosebleed around a girl.

I tend to believe that even if something is bad, it's fine to be an unashamed fan of the parts that you like, and that you should wear your tastes with pride even if they're unconventional. Because of that, I don't think I have any anime I'm actually ashamed of liking.

Well, that's what I'd like to say, but actually there is one, though it's a manga rather than an anime. As someone with an extremely low tolerance for ecchi (I'm not attracted to ladies), my one shameful fave is Nana & Kaoru, which is basically softcore porn. I'm honestly not sure how I got through the first few chapters, but once you get into it holy shit the character depth and the way that the ecchi scenes inform and develop the relationship between our leads. It's so well written, oh my god. But on the surface the whole manga is just boobs, butt, and bondage, and I swear that's not what I'm there for, lol.