I wrote the following as part of my application to my first design job. It was for a mobile game developer; I didn't know much about mobile, but I downloaded a few free demos, tried them out and explained my opinion and general approach to design. Given what I know now, I think I damn near nailed it.

Most mobile games have very little replayability.  I do not know if gameplay is as important for mobile games as it is for console games but I will assume that it is.  Fundamental to replayability are continued challenge (the potential for greater achievements or higher scores) and novelty (new things that happen).
There are basically three types of games:  games that are puzzles, games that are toys, and games that lead a user through a story.  Many computer and video games combine two or all three of these types. 
A puzzle is something that, once solved, provides a significantly smaller challenge the second time it is played.  A puzzle can be as simple as recognizing a pattern.  Randomization is the only way to make a pure puzzle replayable (the other way is through a complexity so great that it ostensibly random).  Tetris is a pure puzzle game in which the next block provided to the user is randomized.  Prince of Persia is a game which has puzzles (such as stepping on a switch to open a door).
A toy is something that often requires little thought but provides entertainment and allows for user improvement.  Usually a toy involves reaction and eye hand coordination and progress if often measured with a score.  Tony Hawk pro skater, Tekken and Snake (aka Nibbles or worm) are examples of toy type games.  A toy would also be any game which has no specific goal, like the sims.
A story game often involves levels and reveals the story to the user in installments; this includes most platformers, adventure games and RPGs.  A story game often loses appeal after the first play through because the player already knows the story.  Ideally the player tells his own story and the game is more of a story telling toy that is different every time.

What I see in mobile games are predominantly puzzles and toys.  The puzzles are mostly recreations of existing puzzles that were easily ported to the mobile platform.  In my opinion, these are the most solid games.  The toy games are an attempt to take existing platformers, driving, sports and action games and scale them down to mobile size, mobile button control and mobile complexity.  Most appear to be failures; they are neither fun nor true to their progenitors.

A serious problem facing mobile games seems to be receiving user input.  Perhaps, because I am more accustomed to platform and computer games, I face a steeper learning curve, yet I imagine problems must arise from the simple fact that not all mobile phone’s buttons are arranged in the same way.
I think that more design consideration needs to go into simplifying the user input.  This would also make the games more immediately accessible as the user would not have to read about and memorize many different buttons.
I wonder if there is any standardization to mobile games and can all phones be expected to have arrow buttons?  Menu options (where possible) seem to be the most intuitive means of taking user input as almost all phone users know instinctively how their phone navigates and selects.

Verizon games

Buddy Bass Fishing

Where this game succeeds:
The graphics are nice, the pond map is serene and the different location names are cute.  The boat view and water view graphics of the water, the fish and the debris are all nice and give the user the feeling of actually sitting in a boat, fishing.  Reeling in a hooked fish requires skill which the user can develop through further play and there is a certain amount of excitement as the user attempts to balance line tension and navigate the fish around obstacles.

Where this game fails:
The variables (lure type, weight, “snap” and location) all seem irrelevant.  Regardless of the lure type and weight you choose, you will catch fish with the same regular frequency.  The snap value is a complete mystery to me but I don’t care because high and low snap seem to do the exact same thing.  The location I select also seems to be irrelevant.  Although there are eight locations on the lake to choose from, they all have the same look, the same types of debris and the same density of fish.
Hooking a fish is too easy, and reeling it in is too hard.

What I would change :
Each lake location should be distinct – it should have a theme, even if this meant as little as, “Meyer’s Point” doesn’t have an eastern quadrant because there is land there.  Changing water color slightly and setting debris themes (a “Craggy Coast” could have more rocks and fewer plants) can have a big impact in making the location variable mean something to the player.
Fish should be harder to find.  From the boat view, the player should have to search for the subtle signs of a fish moving around under the surface.  This would help make finding a fish more exciting, successfully reeling in a hooked fish more important and encourage the player to change locations.
Getting a fish to bite should depend on the variables and the effects of the variables should be clearly defined.  When the user is selecting a lure type an information box should say something like: this shiny lure attracts fish even in darker waters although it should not be used too far under the surface.  Now the user knows that Spooky lagoon might be a good place to use the shiny lure and that he should use it with a light weight.  Another idea could be a fuzzy lure that is more likely to get a bite but is also more likely to get caught in reeds.

Prince of Persia

Where this game succeeds:
This is a very true port of the old game.  It is recognizable and easily picked up with a minimal amount of experimentation.

Where this game fails:
In the original Prince of Persia, if the user presses and holds right or left the prince dashes in that direction.  When using a phone key pad, this becomes difficult to control and I often killed the prince accidentally.
The level design has problems.  The user reaches an iron grate barrier just as the game explains to hit the 5 button to draw your sword.  This is because the first enemy is on the other side of the grate.  The designer made the dual mistake of not explaining what door switches are and introducing them simultaneously with enemies.   I assume that if I am being told to draw my sword that this is the next thing I must do.  Eventually I accidentally stepped on the switch, which was three levels up, and serendipitously fell down to the door which was now miraculously opened.  Had I not played Prince of Persia before I would be at a loss as to what had happened.

What I would change:
The level design needs to be modified to accommodate new and veteran users.  Prince of Persia puzzles are simple and the original game stands as a perfect example of successful design.

NHL Hockey

Where this game succeeds:
Movement and sliding physics worked alright.  The game automatically changes the player to be the nearest to the puck.

Where this game failed:
This game was awful.  It was not immediately clear how to interact with the puck, yet the 2 minute demo time meant that I would have to forgo the instructions if I wanted to play.  Gameplay and AI were both primitive and a mockery of real hockey games.

What I would change:
This game only needs 5 buttons, the four directions and a stick button.  Tapping the stick button would attempt to steal (although slow your player) or pass/shoot the puck in the indicated direction.  A sixth button, check/boost, could be used to give the player a sudden, small burst of speed in the desired direction and allow him to check or to escape a tangle with a defender.
The whole game should be slowed down.  The ice rink is not big enough for the current game speed and the mobile system is simply not robust enough to make hockey a high-speed finger coordination game.  Despite the limitations, the spirit of hockey could be maintained if the game speed was reduced.

Questions:
I was told that Brand is important.  What about creating your own brand?
How important is continued use and user enjoyment?
Where do the games make money?  At purchase, through continued use?
How does a game get placement in the lists provided to the cellphones?
How important is a small barrier of entry / learning curve?  Are demos important?  Why are demos time bound rather than feature bound?
Why do most mobile games lack character and personality?
How important is novelty?  Does the small barrier of entry inhibit novelty and innovation?