Here's another one on sale for the Kairosoft fans, Pocket Stables ($1.20; Regular price $4.99):
https://play.google.com/store/apps/details?id=net.kairosoft.android.horse_en
Gemini Rue and
Shivah are both Wadjet Eye adventure games, and are pretty good choices if you haven't already played them on PC. There's also Amanita's
Machinarium, short and sweet. Double Fine's
The Cave, which has been hit-or-miss with people.
Superbrothers Sword & Sworcery, a highly-regarded game when it was released.
If you want ports of classic adventure games, there's also Revolution's
Broken Sword Director's Cut and
Broken Sword 2 Director's Cut (and the recently-released Broken Sword 5:
Episode 1 and
Episode 2). And of course, Jordan Mechner's
The Last Express.
There are also some notable quasi-adventure games.
King of Dragon Pass is a classic clan-management RPG/Strategy/Sim where you're tasked with some important decisions at certain points.
Sorcery! and
Sorcery! 2 are based on a series of choose-your-own-adventure RPG books; you make a bunch of decisions that determine which paths you take, who you fight, and how you fight. They have a nice style that frequently pay homage to their CYOA origins.
EDIT: Oh, forgot one.
Layton Brothers: Mystery Room is more Phoenix Wright-lite than Layton; it's fairly short and simple, and doesn't take off the training wheels until the last few cases, but it's got a jazzy soundtrack (from Yuzo Koshiro), an interesting overarching mystery, a nice graphical style, and it's only $5 for all of the cases. Well worth the money, even with its flaws.