Are there any good games out there set in the kind of dystopian future you see in TV shows/movies like Dredd (the remake with the big skyscraper) or Altered Carbon or 5th Element or Total Recall (the original, not the crappy remake) or similar?

Yes. Even a free one and very good too: https://www.gog.com/game/beneath_a_steel_sky

And, of course, if you're looking for something like Judge Dredd, then how about Judge Dredd? https://www.gog.com/game/judge_dredd_dredd_vs_death

Dex (and any cyberpunk themed games) might fit too: https://www.gog.com/game/dex it even has a Demo, so that you can try it for free.

and if you don't mind a bit of magic mixed with your dystopia, give the Shadowrun series a try: https://www.gog.com/game/shadowrun_dragonfall_directors_cut

Chaser has been described as Total Recall: The Game.

Honestly, too many. I'mma throw Final Fantasy 7 out there just to screw with the metrics.

The Fallout games although whether Fallout 3 is a good (Fallout-) game is debatable.

To be honest: every game's "goodness" is debatable.
Because whether something is considered "good" or "bad" is always subjective, and we all find different things to be "good" or "bad".

Blade Runner?

Syndicate or Syndicate Wars. That one has a funny intro.

ht/tps://www.youtube.com/watch?v=EJO_pBML7xw

Perfect Dark
Omicron: The Nomad Soul

The Longest Journey.
DreamWeb.
Hellsinker.
Hard Reset.
Technobabylon.
...lots of them!

Messiah
Anachronox
Project Eden

Including a few debatable ones:

Cyberpunk 2077
Deus Ex series
State of Mind
Mirror's Edge
Inside
Dishonored series
Event[0]
P.A.M.E.L.A.
Dry Drowning
VirtuaVerse
Horizon Zero Dawn
Metro series
Omikron: The Nomad Soul
Requiem: Avenging Angel
Messiah
Observer
Red Faction series
Ruiner
SOMA
Spec Ops: The Line
The Surge series
Syndicate series
The Technomancer
Mars: War Logs
Terminator: Resistance
We Happy Few
Wolfenstein series
Firaxis' XCOM series