There are a few attacks in the Super Smash Bros. series that are explosive-type. They are strengthened by Explosives Attack stickers. The vast majority of explosive attacks set targets on fire, with the only exceptions being Ivysaur's bulb blasts (they are Explosive/Grass instead).
Note that, since the concept of type does not exist in games before Super Smash Bros. Brawl, only Brawl hitboxes are included in this list. For example, while exploding carrier items in SSB64 or Melee could be considered explosive attacks, they are not coded as being so.
List of explosive attacks by characters
Other attacks (e.g. Grenade Launcher) cause explosions, but as they do not appear in the Subspace Emissary, they were not coded to deal explosion damage (the data would have taken up no more space). Some other attacks which involve explosions are not explosive-type because they are of another type (e.g. Ganondorf's up tilt is Leg-type).