Some old games have been brought back from the past on modern platforms with good ports. This topic is not about old games emulated on modern platforms (in example scummVM, dosbox), but about old games with actual mobile ports for Android or iOS. I guess what I'm suggesting here is kind of a recommendation thread for good conversions.

I'll start with a couple oldies I've played and which I've found are pretty good.

Broken Sword: Directors Cut. What can I say, tablets have been made for point and click games. Good conversion that works well and is enjoyable to play with a tablet. I haven't played BS2 on a tablet, but I'd be surprised if that was any way poorer port.

Z-Origins: Mobile version of the fast paced startegy game "Z". Works very well and the fast pace makes it an ideal mobile game, that is enjoyable even on my phone screen. Personally I think it works better on tablet than it ever did on a computer.

Dragon's Lair. Simple QTE game that is considerably less annoying on a tablet device than it's on a computer.

Carmageddon does have an Android port and demo version as well. But personally I wasn't sold by it. But then again it was pretty poor demo. Only one car and one track.

Here are some games available on mobile format with origins on the PC, quality varies

King of Dragon Pass
Lords of Midnight
Anodyne
Alien Shooter
Majesty
Doom
Wolfenstein 3D
Battle For Wesnoth (iWesnoth)
Mutant Mudd
Organ Trail
Oregon Trail
Gemini Rue
Cthulhu Saves the World
Lara Croft and the Guardian of Light
Sword of Fargoal
Home - a Unique Horror Adventure
Raiden Legacy
The Bard's Tale
The Howler
Fairway Solitaire
Cubemen
Akalabeth
Sid Meier's Pirates
Civilization Revolutions
Worms
Worms 2
Shadowrun Returns (coming to mobile)
Monkey Island
Sam & Max
Back to the Future
Z
Ascendency
Pitman
Ultima Forever
Savant Ascend (coming soon to mobile)
Two Worlds II Castle Defense
Leisure Suit Larry
Grand Theft Auto III
Ultimate Mortal Kombat 3
Avernum 6
Avernum: Escape the Pit
Avadon: The Black Fortress
Cardinal Quest
Warhammmer Quest
Sine Mora
Dink Smallwood
Shadow Warrior
Duke Nukem
Karateka
Gobliiins
Myst
Riven: The Sequel to Myst
Dracula
Command & Conquer
Dead Rising Mobile
Resident Evil 4
Simcity
Star Wars - Knights of the Old Republic

Edit: These are all on iOS, Android possibly...

Wow, both Z and Carmageddon on Android. Too bad my screen is too small.

https://en.wikipedia.org/wiki/Theme_Hospital#Android_OS_port

The 7th Guest and The Last Express are on iOS. I don't know how good the ports are, though.

GTA3 has been converted to tablets and it works surprisingly well. I played it through without huge issues, though the frame rate was a bit all over the place on my tablet. Vice City has a port as well, but I've not tried it.

Thank you very much for that list +1 :) I've recently purchased my first smartphone(android) and have been looking for "good" games to play on it :)

I enjoyed Plants vs. Zombies on tablet more than on PC. It's fun on the PC but just so suitable for touch. I have some more games with both PC and Android ports, but I haven't played them much.

I'm looking forward to Shadowrun Returns and Deus Ex: The Fall.

Oh, and there are quite a few hidden object adventures on mobile. I like this type of game and it translates well to mobile.

2nd Edit:

You can install DosBox and ScummVM on Android to get old games to work. My experience with these isn't that great, because keyboard controls and right mouse click don't translate well. I installed Eye of the Beholder 2 recently using ScummVM on my Nexus 7, and it works well but combat uses right click almost exclusively, which means I die a lot. Some tweaking of the input method could probably make it a lot more playable, but unfortunately it's not currently available in the Android port. Might work better for turn based games though. I played some Gabriel Knight 1 in DosBox Turbo and it was an okay experience. Still would be better on the PC (but I have less tolerance for 320x200 graphics on the PC).

Also try Ur-Quan Masters (Star Control II).

Star Wars: Knights of the Old Republic. I've given the iOS port a good run and it's pretty damn good.

Sid Meiers Pirates. Another nice conversion to iOS but I haven't had the chance to play it much yet.

I tried GTA3 but hated it, I'm really not a fan of touch controls for third/first person action games.

As I said in the OP this thread is not about emulated games via dosbox or scummVM, only native ports.

Well, Ur-Quan Masters is a native port, and worth checking out.

By the way, I felt that Broken Sword was slightly inferior on the tablet, although it certainly was enjoyable.

Thanks for the list, I was also looking for some!

Imperium Galactica II has been officialy ported to iPad by the original devs.

Final Fantasy 1 to 6 are available on iOS and 1 to 4 on Android.