One great thing about the iPhone / iPod Touch is that there's a whole array of simple games that offer enough challenge to keep us coming back for more time and time again. Running games are a type of simple one button game that asks "how far can you get?" One play can last anywhere between a second and hours, depending on how good you are at avoiding obstacles. If they're good enough you'll keep returning to try and get a little further or beat the high score. Here are several great running games for iPhone and iPod Touch that need your attention (in no particular order):
Monster Dash
Halfbrick Studios | 59p/99c/0.79c

Barry Steakfries is his name, running and shooting monsters is his game. With five monstrous worlds, with unique monsters to go with, Steakfries must equip a shotgun and run as far as he can through the worlds one after another and through them again, disposing of anything that gets in his way. Along the way there are some awesome weapons to picks up including a submachine gun jetpack, as well as the Badass Hog motorcycle. Every 1000m you'll switch to another world and progressively move a lot faster. Shoot, jump, repeat. A true App Store masterpiece.
Canabalt
Semi Secret Software | £1.79/$2.99/2.39

Much the same as Monster Dash, but with no shotgun and no monsters. Delivered with great sound and nice visuals, you must run as far as you can across rooftops. To maintain speed and ultimately stay alive, you must jump over gaps, boxes, falling debris, through windows and off crumbling buildings. Have a go for free over at the official website, and you'll soon be wanting the game in your pocket: www.canabalt.com.
Zombie Highway
Renderpaz | 59p/99c/0.79

Zombie Highway is exactly as it sounds. You take control of a car, plus the gunner in the passenger seat, and you must drive as far as you can up a debris and zombie filled highway. You can twist, turn, squash, knock off and shoot off, but whatever you do, don't hit a wall and don't let the zombies topple you over. With various zombies and plenty of quality weapons to unlock, Zombie Highway will have you revving up the engine and equipping the shotgun time and time again.
Get To Tha Choppa!!1
so so dev games | 59p/99c/0.79

You may be fooled into thinking this game contains Arnie, and perhaps even a Predator, but you'd be wrong. While the aim is to get to tha choppa, you'll never actually get there. You must stay alive as long as you can, avoiding the chasing zombies. The simple actions involve jumping over land mines, shooting approaching zombies and ducking under the helicopter's missiles. Presented in hand drawn style, Get to Tha Choppa!!1 has enough charm to bring you back many times to see if you can finally get to that bloody choppa!!1
Dead Runner
Distinctive Developments Ltd | 59p/99c/0.79

The only running game on the list that's presented in first-person perspective, Dead Runner is a haunting little game where you need to run as far as you can between trees and gravestones. The further you get, the faster you get. Hitting a tree will end your game. Presented with dark and haunting visuals, and eerie music, Dead Runner is best played with head phones. If you're in the right mood you'll feel like you're being chased. By what is for your imagination to decide. I've seriously had nightmares exactly like this.
Run
Arthur Ham | 59p/99c/0.79

One of the lesser know running games on the App Store, Run offers more than most. While the game is based on how long can you last, your reactions play a crucial role. Everything, and the kitchen sink, will appear to end your run at some point throughout the game, including sharks, aliens, saws. To combat this you can fire, punch, jump and slide. It's a very challenging game, but challenging is just how we like our games, right?
Robot Unicorn Attack
[Adult Swim] | £1.79/$2.99

Indisputably the weirdest of the bunch is Robot Unicorn Attack, of which there are two versions, the original and the heavy metal. Both are the same game however, with a different theme, one all dreamy and cute, and the other set in Hell. Your unicorn has to jump and dash through the platforms and go for as long as possible. What makes Robot Unicorn stand out is the strange choice of soundtrack. You play the original with the music of Erasure's "Always." Or you can opt for the Heavy Metal version for some German industrial. Both = Win.
Mirror's Edge
EA | £2.99/$4.99

Everyone's favourite console free running game is equally as great on the small touch screen. Unlike it's first-person bigger counterpart, the iPhone version is third-person. The aim is to jump, duck, wall run and take out the enemies along the rooftops. Unlike the other games in this list, Mirror's Edge is level based. Not that we'd hold that against it.
Did I miss something? Feel free to add it to comments.