The following items can be set ablaze.

Bleak House Flag in Strong Sad's room, after escaping (required to progress).
Bleak House Constitution in Strong Sad's room, after escaping (required to progress).
Bleak House Bill of Rights in Strong Sad's room, after escaping (required to progress).
Smoke detector in the living room of Strong Bad's house.
Strong Bad's bed in Strong Bad's room.
Kimono on the wall inside Pompomerania/Club Technochocolate.
Paper mache skulls in country during Strong Mad sequence (required to progress).
Lonely skull in country near the flag.
Lonely skull in country near where Strong Mad starts.
Bush at the Homsar Reserve.
Candles in the KoT's castle.
UN model in Marzipan's backyard; after winning.
Board game in Strong Badia.