Another reason why these games are hugely succesful is, according to me, the repeat-playing aspect. Having to play a level over and over again until it works out for you. Best example is my favourite iOS thus far: Tiny Wings. Super simple gameplay, very very straightforward, insanely repetitive but amazingly fun.
This is very true. I also think the gradual increase in difficulty makes it a lot easier to get into a game.
I've done a small test with my oldest son, who is now 9 years old. He was instantly into Angry Birds, without any real difficulty. No frustration either, and he finished all levels without much effort.
A few weeks ago I introduced him to my old MSX2 computer and games. Loaded up some vintage 8-bit games (e.g. Treasure of Usas, Vampire Killer, etc) and asked him to start playing. Well, he was quite frustrated after some time because these games were so damn difficult to get into.
The lack of graphical possibilities were clearly compensated by a much steeper learning curve. Of course, hand-eye co-ordination was difficult too, with the keyboard arrows and space+alt keys..
Angry Birds can be scored easily, you only need a bit more effort if you want to play for 3 stars. Vampire Killer was full out, and after 3 strikes you're out. Starting over again, losing your progress.
So, it's a combination of easy learning curve, easy progress and fun controls that makes the current games so popular.
This is a good thing. But sometimes I look back at those good old days and pretend we were much better gamers than the current generation...