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
Unfortunately, unlike with other mobile platforms, the traditional Bluetooth mobile controllers available on other platforms can't be used on iOS:
- MSI BGP100 Bluetooth Gamepad
- WiiMote
iCade / iControlPad for the rescue! These two controllers both work without having to jailbreak your iDevice and with a sizeable number of recent, sometimes top-quality games and not only not very good, clearly outdated ZodTTD emulators.
iCade (homepage

(Note that the iCade has two spin offs, the Atari Arcade and the Invadercade
iControlPad
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?
It's pretty easy: all depends on where you want to use them and with what device. At home, with an iPad, and you prefer arcade cabinets with huge, robust joysticks and fire buttons? iCade. On the road (when, say, commuting to/from work/school or on a long trip)? iControlPad. If you can order the iCade and prefer the arcade cabinet approach to handheld controllers, go for it. If you prefer the latter, go for the iControlPad instead.
As a cons, it must be mentioned that, except for some already-linked exceptions (e.g., Atari and their old arcade stuff), only indie developers seem to be adding Bluetooth support in their games. I'm not sure big names like Gameloft or EA will ever add support. Nevertheless, the (relative) rarity of games supporting these controllers also means you don't end up wasting too much money on them. (Some three months ago, immediately after receiving the iControlPad, I only spent some 20-25 euros purchasing all the still missing, compatible titles. This also means I, as has also been hinted at in the title, will at least try to continue this article series.)
My favourite iCade / iCP-compliant games
Let me list you four of my favourite games. (More to come in the next article instalments!)

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
More info: TA thread

My special, never-before-published tip, particularly if you plan to get a decent position in the OpenFeint / Game Center (GC) score list: as you can see in the second half (between 3:38 and 3:56) of the video below (the first half of it shows Vertex Blaster), if you have the iCade, then, making use of a bug in the game, you can make the worm just move right on the surface, unlike with controlling the worm with the on-screen controls. This will mean your combo multiplier will quickly raise to even 50-60, meaning quickly collecting a lot of score. Of course, this bug can be used only before surface-based bombs and shooting helicopters arrive; when they do, you'll need to return to the traditional “jumping” approach to be able to shoot down the bombs from a distance or avoid touching them altogether and to be able to shoot at / knocking out the helicopters.
Katana Jack! by Ivanovich Games

One of Ivanovich Games' previous titles, an Operation Wolf
Katana Jack! is, fortunately, considerably cheaper ($1) and, just like, Operation wow
A special feature of the title that every background is manually painted / drawn on the iPad (and the background music is recorded in GarageBand). You can even watch the background being drawn in the videos that get gradually unlocked. (BTW, as far as playing back these videos is concerned, don't fast forward / rewind them while playing back. There seems to be a bug associated with playback position changing.)
Speaking of being everything hand-drawn, the Ivanovich Games folks have also presented me an also (on the iPad) hand-drawn iPhone Life mag logo. It's as follows:


Super Crossfire HD by Chillingo Ltd

While the idea of this game isn't anything new (the game is based on Galaga (Galaxian)
A short and quick-paced trailer:
A game video:
Tutorial: Play MAME games on your iDevice
TouchArcade's List of iPad Games with iCade Support
Speaking of TouchArcade, you will definitely want to follow THIS thread, paying particular attention to the compatibility list in the first post.