With a noun:
* Houseboat: A boat designed to be lived in.
* Greenhouse: A building made of glass for growing plants.
* Playhouse: A small house for children to play in.
* Doghouse: A small shelter for a dog, sometimes used figuratively to mean being in trouble.
* Warehouse: A large building for storing goods.
* Workhouse: A place where people were sent to work, especially during the 19th century.
* Pothouse: A pub or tavern.
* Townhouse: A house that shares walls with other houses on either side.
* Firehouse: A building that houses fire engines and firefighters.
With an adjective:
* Housebroken: Trained to use a toilet.
* Houseproud: Taking pride in one's home.
* Housebound: Confined to one's house, often due to illness.
With a verb:
* Housekeep: To take care of a home.
* House-train: To train a pet to use a toilet.
With a preposition:
* House-to-house: Going from house to house.
* House-by-house: Similarly, going from house to house.
Let me know if you'd like more examples, or would like examples of compound words with different parts of the word "house" (like "house" followed by a different word).