Dino Run is a perfect example of how to create a game with lots of interesting content that will keep you playing for a long while around a very simple gameplay concept. It's also where I earned my very first (and to date only) Impossible badge, so you can tell I liked it enough to stick it through all the way to the end.
The basic concept is based around an entertaining, if scientifically dubious, thought: what if the dinosaurs had been able to outrun the wall of lava kicked up by the asteroid impact? Maybe they would have been able to survive then! So your goal is, quite simply, to run as fast as you possibly can, over hills, through valleys, and with all sorts of obstacles running the gamut from annoying to irritating. (If this reminds you of Danger Swamps, I'm not surprised, but rest assured that this is a vastly better game.) Should you stumble and slow down, fiery doom awaits you, but if you make it to the end of the level, you'll find sanctuary in a cave (or, if you manage to beat challenge mode in the highest difficulty level, a spaceship, but perhaps I shouldn't give that part away...). You're not the only creature running for its survival, though; there are hundreds of other dinosaurs, nearly all of which are also trying to similarly escape their fate, some smaller, which you can eat, some bigger, which get in your way, and some faster, which you can hitch a ride on. There are also pterodactyls flying overhead, which you can grab onto to fly above the fray for a short period of time, but beware the wrong-way pterodactyls, which give the legendary unbeatable(?) pterodactyl a run for its money as the most annoying video game pterodactyl.
The game offers a wide variety of game modes. In challenge mode, you run through a course of 7 levels, beginning with a bright, sunny field and ending in a scorched, blacked, magma-filled Apocalypse level. You can gain more lives by collecting eggs (and hence saving more members of your species), but should you run out, it's game over. There are also "speedruns", which are really just single levels, usually with one feature that makes them stand out (for instance, a large valley, or lots of pterodactyls). Interestingly, no level will be the same twice -- each is randomly generated. It seems that the map is generated from a certain fixed set of chunks of terrain, some which may be large and some which may be small, and certain large features are likely to appear in certain levels, but nothing is guaranteed. For instance, there's a large waterfall that usually shows up in Level 4 of the challenge mode, but it could show up anywhere in the level, and it might not show up at all. This means that practicing a speedrun, while helpful to some degree, won't really help you learn the course (though you can learn to recognize signs of some of the larger terrain features, and some of the chunks are pretty large, so learning them can be useful).
There are four difficulty levels, but starting out on the hardest ("Insane") is literally impossible. Your dinosaur starts out puny and slow; in order to be able to handle the harder difficulty levels, you have to increase his power (just like tuning your car in Gran Turismo, for instance). This is accomplished by collecting DNA, which can either be obtained by collecting eggs, munching critters, or accomplishing various milestones. These milestones represent various degrees of achievement, and often reward you with hefty chunks of DNA or bones (which are used to unlock additional content). Some of these milestones are awarded for various difficult stunts (e.g., "doomsurfing", or staying just barely ahead of the wall of doom, for a given amount of time), while others are awarded for cumulative achivements (e.g. saving a certain number of eggs total). The latter can be kind of frustrating at the end of the game when you're trying to reach all of the milestones -- after finally beating the challenge mode and all of the speedruns on Insane, I still had to go through and collect more eggs and eat more birds. You'd think I'd have already proved I could do that.
The presentation is suitably retro -- the art is very pixelated and 8-bit, and the music similarly so. The sound effects are not bad; the music (as is so often the case) gets a little repetitive, but there are enough different themes to prevent it from being totally boring. The interface is a little odd (sometimes relying on the keyboard and sometimes on the mouse), but when you're playing it's all keyboard. There are also lots of cute little touches -- for instance, you unlock additional colors as you progress through the game, which allows you to customize your dinosaur; donating also gives you access to various amusing hats your dinosaur can wear.
Dino Run provided hours of enthralling gameplay for me, because it has such a large source of generally interesting challenges. While it is by no means an easy game, you'll get better as you play, and there's quite a feeling of accomplishment for making it through to the end, whether it's your first time surviving or your first time on Insane mode. Overall, it's a thoroughly enjoyable game.