Hi, there are several RPG-style games for Android devices, although many of them seem to be designed for small phone screens rather than tablets. Below is a list of some potentially interesting titles. I have not tried most of them, so I can't make any assurances about their actual quality or compatibility.
In addition to the list below, Ossian Studios may be interested in bringing their upcoming game
The Shadow Sun to Android devices too in addition to iPod/iPhone/iPad. According to
a post by producer Alan Miranda on their forums "Android definitely does sound like a good idea to us", however, there's no official announcement for Android yet, and their current priority is getting the game done for iOs.
Now here's the list; the links go to the entries of the games on Android Market. Many of the paid games have a free lite version available (sometimes I've linked to the free version). I've tried to classify the RPG titles based on the style of play, but that's mostly based on very brief looks at the screenshots and game description, so I may have misclassified some of the games. I may also have missed several games. Also, I've only looked on Android Market, there might be some RPGs available elsewhere.
Action RPGs:
Dink Smallwood HD
Zenonia
Zenonia 2
Zenonia 3
Inotia 3: Children of Carnia
Legends Arcana
Cyberlords - Arcology
Emissary of War
Dragon of the Three Kingdoms (not sure how strong RPG elements it has, described as an "Action RPG (arcade beat'em up)")
Flailery RPG
Galaxy Hero (described as a "top-scrolling shoot-em-up RPG hybrid"; does seem to have several RPG elements)
BRAVE
Across Age DX
Destinia
Illusia
Colosseum (described as an RPG, not sure how strong the RPG elements are)
Also worth mentioning is
The Ur-Quan Masters (an open-source version of the original commercial game Star Control II); it's debatable whether it can be called an RPG but it has some RPG elements.
RPGs with pauseable real-time tactical combat:
GemRB (Thanks for noticing this Motoki! Implementation for running Infinity Engine games like Baldur's Gate on Android devices.)
RPGs with turn based battles (Final Fantasy style or other turn based system):
Gailardia
Spectral Souls
Symphony of Eternity
Project Angel: The Resurrection of Atlantis
Wizards RPG 2
Cyber Knights RPG
Mardek RPG
Mardek RPG 2
Gurk, the 8-bit RPG
Gurk II, the 8-bit RPG
BladeQuest (demo)
Dungeon Wonders
Dungeon Scroll
Puzzle Wars (looks somewhat similar to Puzzle Quest)
MatchHack (battles based on memory matching)
Magic Tower: Save the Princess (perhaps more a puzzle game than an RPG)
Infinite Tower RPG (probably turn-based, not sure how far in development it is)
Acedia RPG ("inspired by old computer games like the Ultima series")
Totally Random Hero RPG
Eve of the Genesis HD
First-person RPGs (full 3D or Dungeon Master -style):
Realms of Fortune
Crusade of Destiny
Deadly Dungeons
Oubliette
Earth and Legend
Roguelikes:
Angband
Angband variants
Roguelike classics (Rogue, Moria, Larn)
NetHack
NetHack tiles pack
NetHack Slash'EM
NetHack Slash'EM tiles pack
NetHack (different implementation than the above one)
Sigmore Mines 2
Voyage to Farland
Andor's Trail
Dweller (beta)
Legends of Yore
Hydra Slayer
TraqueHack
No Way But Down
Quest: Swords and Spells
Infinite Dungeon
Kamyran's Eye
We can beat GIANT MONSTERS ES
Gamebook (multiple-choice) style games, some of them might contain some RPG elements:
Choice of the Vampire
Choice of the Dragon
Choice of Broadsides
Choice of Romance
Imprisoned
Choose Your Path Free
Alter Ego
Zombie Chronicles
Zombie Chronicles 2
Also, Tin Man Games, who make
several gamebook titles for iOs, seem to be bringing their games to Android devices; in a recent post on
their blog they wrote "Also to all Android phone and tablet users – we are coming to Android later this year – watch this space."
There are also several online RPGs, for example:
Order and Chaos Online (looks similar to World of Warcraft)
Pocket Legends
Star Legends
Warspear Online
World of Dragons
The Mana World
Empire Online (update Oct 9, 2011: seems to be no longer available)
Dragon Collector RPG
Elemental Knights Online
Aardwolf RPG (text-based, multi-user dungeon "MUD", somewhat like an online roguelike)
BlowTorch MUD Client (not a game, just a client for playing several MUD games)
AndroMud (another MUD client)
Urban Dead for Android (frontend for existing web-based zombie game, proof of concept)
TibiaME MMO
Faintless MMORPG (in development, pre-alpha)
Explorer Heroes
Strategy games with RPG elements ("Tactical RPGs"):
Knighturn RPG (seems to be a strategy game with some RPG elements)
Swords & Earrings (seems to be a strategy game with some RPG elements)
Battle for Wesnoth (Thanks for noticing this Arhu!)
Mage War
Free Heroes 2 (Thanks for noticing this Lucky Day! Implementation for running Heroes of Might and Magic II on Android devices; in progress. The Heroes of Might and Magic games are strategy games with some RPG elements.)
VCMI (Thanks for noticing this Lucky Day! Implementation for running Heroes of Might and Magic III on Android devices; in progress. The Heroes of Might and Magic games are strategy games with some RPG elements.)
Trading/strategy games with RPG elements (like Elite/Privateer):
Pirates and Traders: Gold!
Star Traders RPG Elite (a "complex space simulation and turn-based Strategy role playing game", might be closer to Elite/Privateer style games than traditional RPGs)
Note that there are lots of massively multiplayer online games that are somewhat similar to the above genre, involving resource gathering/management and possibly some combat/strategy. They are sometimes named as RPGs, sometimes just massively multiplayer games without an RPG reference. I've listed some of these below:
iMobsters,
Mafia Conflict,
Zombies Live,
Vampires Live,
Kingdoms Live,
Ninjas Live,
Zombies RPG,
Algadon Medieval Web Game,
Phoenix Emperor,
Project Galaxia,
Dragon Life,
Age of Legends,
Dark Galaxy,
Villains,
Roman Empire,
Crime Inc,
Superheroes Alliance,
The Streetz,
Emross War,
Universe War