These might be closer to mediocre than BAD bad but I don't expect too many people to mention them so why not.

• Drakengard 3 - action adventure game with dated graphics (even at the time of release), terrible performance on the original hardware, huge amount of asset reuse (including whole levels) and writing that can range from childish, crass and annoying to extremely emotional. It's rough but it's also my favourite Yoko Taro game.
• Ghost in the Shell: Stand Alone Complex (2004, PS2) - alright gameplay, decent voice acting, meh story and levels. It's not terrible but based on the opinions I've seen it seems like I enjoyed it a bit more than most. Pretty cool drum & bass soundtrack.
• Kane & Lynch (both games) - most people didn't like these games due to rough feeling gameplay and presentation (especially in the first game), I can't help but love it. I feel like all of the elements combine in a coherent and extremely raw experience which might not be "fun" or "polished" but for me it just works.
• Kao the Kangaroo (2000) - extremely basic mascot platformer with (mostly) dated visuals, linear levels and some annoying enemies. Sequel might be an improvement but I still prefer this ugly duckling over anything that came after.
• Oni (Bungie's action game from 2001) - it has huge empty levels, basic presentation, pretty mediocre story and uneven difficulty curve. It also has a great hand-to-hand combat system which makes those issues easier to swallow. Pretty good Ghost in the Shell game.
• Scarface: The World is Yours - GTA clone set after an alternative ending to the 1983 movie with Al Pacino. Pretty ugly and rough around the edges but it also has some fun mechanics (empire building, customisable mansion, money laundering, ability to bribe cops and more). A competent experience, even if it didn't reach the heights of GTA or Saints Row titles.

Edit: I remembered another one!

Trespasser - physics based action-adventure game from 1998, intended as a sequel to The Lost World: Jurassic Park movie. It has extremely weird and wonky control scheme where you interact with the world by moving your hand - as in, you physically move it with your mouse, no simple "press button to do things".

• You want to open the door? Cool, use your hand.
• You want to make yourself a ramp using a plank? You know how physics work so go ahead.
• Interacting with keypads? Just push the buttons.
• Want to attack something with melee? Pick up an object and swing manually.
• You want to aim your gun? No crosshair, move the barrel in the general direction of your target and pray it'll work.

It's not super intuitive but it does work pretty well once you get the hang of it. Heck, I even managed to throw a 3-pointer at the court in the residential zone! Man, I wish I still had my Twitch account...

The game also went with a "no hud" approach so no ammo count (only vague call-outs by the character like "about 5 shots") and to check your health you had to look at the tattoo on your chest (it changed depending on your HP). Also no gun reloading cause your other arm is broken and your character can't do it one handed, I guess.

It was unfinished, extremely ambitious (both in terms of planned features and implemented technology) and has a bunch of problems. It's an interesting and very unique experience, worth a try even today in my opinion. It's also the only piece of Jurassic Park media I actually care about and I wish it was easily obtainable in official distribution again - come on GOG, you can do it!