This works similar to "What Video Game am I?" with a few exceptions:

1.  You have to follow the rule of the ABC game: Your video game has to start with the letter after the first letter of the videogame before it.  For example, if I were to pick Ape Escape and it were guessed, then you could pick Balloon Fight as your game.  Common words such as "and" and "the" do not count towards the first letter of the game.

2.  You have to choose a game from a different system than the one preceding it.  For example, if the previous game was for Dreamcast, you cannot choose a game from the Dreamcast library of games unless the game was also made for a different system as well.

3.  No games are allowed that include vulgarity, suggestive material, etc. in their name.  Also, don't include any hints that are vulgar or suggestive in nature.

4.  Finally, have fun!  You MUST have fun.

I'll start this off: A is for a game that a video game that few have objections with.

Could you please elaborate on this some more as this is way too great of a deviance to what your trying to get across there are way too many games out there that begin with an "A"  that people don't object to. And you didn't even give a system as to that the letter is too, so I am going to make a guess and say the game you are talking about is advance wars for the Game boy advance
Now I am going to modify your rulings,

1. The system can't be used twice in a row,

2. You have to give a system that your game is on,

3. And you need to give a small description of your game..

my turn- B

mine is on the NES, and you play as a dinosaur that shoots bubbles.