Classic bomberman has the player in a maze with filled with enemies and blocks. Some of the blocks can be destroyed. A level is finished by killing all the enemies. The player clears terrain, pick up powerups, and kills enemies. Bombs explode in a cross shape. Explosions cause other bombs to explode. Multiplayer is the most fun part of it. It looks like there are many flash clones on the Internet so you should check it out.
In a skillset there would be a bomb skill, a fire bomb skill, a ice bomb skill, holy bomb skill, and a bomb mastery skill. The bomb's explosions be able to explode other placed bombs or terrain that exists in the level.
Teleport bomb might be interesting too. In Zangband you spend a lot of time positioning yourself with teleports and speed. A teleport bomb could clear enemies without killing them or move the player around.
There are some enemies in Zangband that explode. Orc Sappers are weak enemies that explode when they die. The interesting part about this is that orcs spawn mostly spawn in huge groups. So multiple sappers can die at once from friendly fire damage from sapper's explosions or orc mage's fireballs. The player has to choose his position carefully. In lucky situations most of the orcs can be killed in a big chain reaction.