Hm. Genres I tend to skip because I'm not that fond of them include strategy, simulation, sports, HOGs, visual novels, stealth games, survival horror, beat 'em ups, military shooters (more a theme than a genre), MMO's, JRPGs, maybe rogue-likes and ARPGs (I don't really dislike the latter two, I just get bored with them rather quickly). Let's see if I can find some games in these genres that I enjoyed ...

Strategy:
Blue Libra (because it's simple and casual, easy to learn and maps don't take much time to play through)

Simulation:
Startopia
Theme Park (both mostly because of the funny setting)

Sports:
Super Star Ice Hockey (1987) :D (played as local co-op, good memories)
[I also like wacky kart racers, but I guess they're more like arcade games than sports]

HOGs:
Tiny Bang Story (no 'traditional' hidden objects screen though, in the sense that you'd get a list of mostly unrelated items to spot for no reason, and those are mostly what I hate about the genre; on the other hand, there's no real story either, but it's relaxing)

Visual Novels:
To the Moon (if that counts as one, since you can move in it)
Soul Gambler (because it's like a comic book with lots of choices, as opposed to just displaying long prose to read and prompting for "Press a key to read next batch of text")

Stealth games:
Dishonored (also a FPS of sorts though)
Mark of the Ninja (also a platformer though)
Gunpoint / Ronin (likewise)

Survival Horror/Zombies:
How to Survive

Beat 'em ups:
Tekken 3 (PS2)
Castle Crashers

MMO's:
Some persistent worlds (PW) for Neverwinter Nights
(e.g. Hlontar Adventures, Prisoner of the Mists, Arbor Falls; no idea if they're still online)

Military Shooters
Mass Effect ;P

JRPGs:
South Park: The Stick of Truth
Die Reise ins All (German Freeware)
Chrono Trigger
Fortune Summoners (if that counts as a JRPG, it's partially a platformer and removes the static turn-based menu combat I dislike in JRPGs)

Rogue-likes:
I seem to prefer rogue-like-likes that cross over into action genres, like
Tower of Guns
The Binding of Isaac
Tallowmere
Hand of Fate (although I'm sure if I would call this rogue-like-like)

ARPGs:
Nox (it's been a long while since I've played it, so I don't know whether I'd still think it's special today, but it's one of the few ARPGs that I managed to play through; the reasons for this might be a shorter playtime, less randomization and the additional use of keyboard as opposed to just clicking two mouse buttons)

In general I notice I'm pretty conservative about these genres though, most games I play and enjoy are from the same genres not listed here (CRPGs, point-and-click adventures, platformer/metroidvania, FPS etc.).

I don't like FPS games but I really enjoyed AvP 2 especially alien part

Roguelikes (that come in the disguise of r-lite platformers):
Spelunky
Rogue Legacy
Vertical Drop Heroes

Arguably that may mean I still dislike 'real' roguelike games, since I've yet to play one that I actually enjoy.

I generally find online multiplayer shooters very boring (e.g. Counterstrike, Crysis 3 multiplayer, Quake deathmatch, etc. etc., the ones I've tried)... except the TeamFortress line of shooters. I really much enjoy playing them for some reason. I started playing TF already with the early Quake TeamFortress, later also Quake MegaTF, and then migrated to TeamFortress Classic, and nowadays TeamFortress 2.

I guess it is e.g. because of the nine playable classes which are very different to each other with wildly different gameplay styles. Heck, when you play the engineer class, the game is basically a glorified tower defense game!

EDIT: One clarification, in e.g. TeamFortress 2 I mainly enjoy just "Capture The Flag" and some "Capture Point" kind of maps. I generally don't like e.g. Payload Race type of maps in TeamFortress 2. Nor those "special maps" e.g. that one medieval map where you can only use "mediaval weapons" (meaning that sniper has the only ranged weapon (a bow), other classes have to use melee weapons like swords or whatever). That map makes many of the classes quite useless, destroying the very thing I like in the game.

2D platformer games: I don't generally find them interesting, but for some reason I enjoyed playing and completing LIMBO.

3D platformer games: Same as above, but for some reason Croc: Legend of Gobbos found its way into my heart. I even like its tank controls (a bit like the controls in the first Tomb Raider game actually), compared to e.g. Spyro's freeform controls.

Managerial games (football manager, Simcity, Theme Hospital etc. etc.) are also one genre where I just don't see the point of playing, but somehow I feel there might be games there I'd enjoy, considering I do enjoy e.g. RTS games. I enjoyed e.g. Dungeon Keeper a lot, can it be considered as a managerial game?

I hate Japanese RPGs but I love Chrono Trigger.

I can't stand sport games, but I really enjoyed tennis on the NES

Hate is such a strong word, but I really dislike racing games and sports games.
But I did enjoy the Burnout series and Nintendo World Cup.

I don't like racing games but I like Carmaggedon? Sure, I'm on the same board there, except I don't think Carmaggedon is a racing game. Sure, you could play it that way, but it's like saying Deus Ex is an FPS; technically true but a completely subpar experience. I like Carmaggedon not despite being a racing game, but because it's an arcade with some racing elements of very little consequence.
I guess I could say I don't like Diablo clones yet I enjoyed Borderlands 2, but how much truth is there to that (under the context of the OP)?

'Hate' is too strong a word, but I've struggled to enjoy MMOs, which I count as a genre.
However the Star Wars The Old Republic mmo was definitely fun.

Post-edit: forgot to include The Crew , which I really liked as well (still playing actually).

Maybe the Super Smash Bros series while I don't like Beat 'em Ups

Overlord

I couldn't even tell you why I bought it in the first place. The genre is given as Strategy - Action - Fantasy and while strategy isn't my cup of tea, I really, REALLY hate fantasy settings. And still, this is hands down one of my favourite games in the gog catalogue. I love monster infighting in action games and this game is basically that for its entire duration. And the setting seems to have been created by people who hate fantasy settings/tropes/clichés as much as I do.

I really don't like to play FPS games unless it's something like stalker call of pripyat or the first prey pc game those games were unique and fun.

Not a platformer guy but played the original Megaman on nintendo 8-bit for about two years of my life.

Oh yeah, I don't like sports games (football/soccer, ice hockey, what have you), but Speedball 2 was and is great, both against the computer and a human player. I don't know why, it just is.