Cadaver747: Right. The same issue Nintendo having with its Wii / Wii U consoles. When a company limits controller input it have to adapt existing games into mediocre ports. Only original games can be profitable.

Imagine if Sony, Nintendo, Microsoft, Apple and all other Android players allowed to connect every USB controllers possible. The world could be simplier :))
Cadaver747: Right, I was insinuating actual controller support. The only game which came into mind is Unreal Tournament 3.

I just can't play Halo or Killzone with mouse & keyboard. Got my point?

deke913: Heroes of Steel
Baldurs Gate enhanced edition
Icewind Dale enhanced edition
Delver

Gerin: HTC make great phones. I'm sure you'll love it.

Shmacky-McNuts: USB Controllers work fine. PS3 also works with Blue Tooth and doesn't need the paid app in order to use it either.

Not sure why people don't test stuff. Half the people I tell this too are like...oh...no kidding they work! lol

deke913: I can use the usb OTG cable with my Nexus 7 2013 with a Xbox PC controller and play most any game. Some give me problems like Ravensword for instance but most work fine.

F4LL0UT: Anyway, thanks for the many suggestions so far, people. Will check some of the games out.

austen1000: There are a couple of unofficial source ports, Star Wars Jedi Knight II Jedi Outcast and Jedi Academy, by Beloko Games, on Android, that I play every now and then. They even support mods from the PC version. But, they also require some files from the PC version.

227: Hitman GO's pretty fun, though I wish it came with a story of some kind. Let's see... I'm just going to go through my apps and list off the ones I liked, so there'll probably be some overlap with other people's recommendations:

80 Days (because it's a well-written steampunk take on Jules Verne's story, and it has a lot of content in it)
Zengrams (a short, but mind-bending puzzle game)
Terraria (the mobile version has some exclusive content, and the controls aren't as bad as I expected)
Buff Knight (a simple little RPG/runner game that's incredibly weird)
Game Dev Story and Dungeon Village (addictive)
LYNE (pretty, minimalistic, and unique puzzle game)
Devil's Attorney (a short RPG-lite with a great sense of humor)
Detective Grimoire (a short, but whimsical and lighthearted adventure game with great music)
Big Action Mega Fight (a 2D brawler that actually handles surprisingly well on mobile)
Tales of Illyria: Fallen Knight and Tales of Illyria: Beyond the Iron Wall (hugely underrated RPGs, with random events, strong stories, and Oregon Trail-like resource management)
Sparkle 2 (a casual match-3 gem-shooting game, but one that's incredibly polished and entertaining)
Virtua Tennis Challenge (it handles better than I expected, and Virtua Tennis is always fun)

There are a few more that come with a caveat like Monument Valley, which is fun and unique, but seriously overpriced for how short it is. Sorcery and The Room also come with a warning that they're short and end midway through their stories, so you'll be roped into the sequels if you want any kind of closure. Personally, I don't think they're worth it.

You might look into DotEmu games that are available on mobile. I haven't played much of it, but their 20th Anniversary edition of Simon the Sorcerer looks like the definitive version of the game and includes many different versions of the soundtrack. They also have The Last Express for sale; I haven't tried the mobile version, but it's totally worth it if it's anything like the GOG version.

madth3: I got this in the bundle and I had no plans to play it but my gf just got a tablet I can borrow so I'll be cheching it out.

F4LL0UT: Yeah... last time I checked people still used the term "handheld" to distinguish consoles from phones and tablets.