Playing without physical controls (buttons), only using the touchscreen, is pretty hard. This includes a lot of game types, particularly ones where quick direction changes are needed and / or you can't make the smallest mistake and must be absolutely sure even the smallest movements on the directional pads (D-pad for short) is registered. In games like these, physical D-pad / button feedback is of extreme importance.
There are several hardware add-ons, one of them (Fling
Current situation
iCade / iControlPad for the rescue!

(Note that the iCade has two spin offs, the Atari Arcade and the Invadercade
The iControlPad is compatible with all iCade games. But not the other way around – after all, the iCade doesn't have analogue nubs, “only” a digital D-pad. That is, you can't even expect iCade to, some day, become iControlPad-compatible and run native iControlPad titles like Vertex Blaster. As the latter (iControlPad) has very few native (read: non-iCade compliant) titles (currently, I know of Vertex Blaster only) and, as has been explained HERE

(iControlPad also showing the universal holder holding an iPod touch. The latter runs the native iControlPad game Vertex Blaster, one of the best games.)
Which one to go for?
Let me list you four of my favourite games. (More to come in the next article instalments!)
Vertex Blaster by Warner Skoch
Do you like Activision's Geometry Wars

It's (not counting in the MAME emulator modified by Les Bird
Note that I would have been able to achieve a much higher score; I was just a bit nervous because of the camera recording so I couldn't concentrate fully on the game. The second half of the video shows the same controller in digital-only (iCade emulation) mode, this time controlling the also excellent title “Mega Worm
This is another excellent, highly recommended title. Unlike with Vertex Blaster (and like with all the other listed titles), it's (also) iCade-compatible.

Katana Jack! by Ivanovich Games

One of Ivanovich Games
A special feature of the title that every background is manually painted / drawn on the iPad (and the background music is recorded in GarageBand

Don't be misled by how easy the first few maps are. The others will be much harder, particularly when you plan to get all the stars on a particular one, which means avoiding death, destroying the lamps strictly in order and trying to kill as many enemies as possible. I've spent even 30-40 minutes with some maps, continuously restarting it when getting killed or not slashing the lamps in order, before I got everything right and all the three stars. BTW, I'm currently the 2nd in the worldwide all-time-bests list:

Super Crossfire HD by Chillingo Ltd

While the idea of this game isn't anything new (the game is based on Galaga (Galaxian) and Space Invaders with some brand new twists), the implementation is just great: great music, great 3D animation, great particle effects, great everything. It's probably Chillingo (the publisher)'s ignoring Game Center (and going for Crystal instead) is the only thing that I find annoying. GC leaderboards please, as with all the other reviewed titles!
A short and quick-paced trailer:
A game video:
A long TouchArcade review definitely worth reading is HERE.
Additional information
Tutorial: Play MAME games on your iDevice (my previous article also showing the iControlPad in action; this time, with the MAME emulator)
TouchArcade's List of iPad Games with iCade Support - in addition to AppStore links, it contains both a short summary of the listed games and also links to (possible) reviews. A gold-mine! (Note that this list isn't necessarily updated on a daily basis. This is why, for example, Katana Jack! (a recent favorite of mine) is not on the list. iControlPad-only (that is, games that can only depend on analogue controls) games (currently, the above-reviewed Vertex Blaster only) aren't listed either.
Speaking of TouchArcade, you will definitely want to follow THIS thread, paying particular attention to the compatibility list in the first post.