Of course, real players don't need any cheats, but they are pretty handy when you want to play through an adventure quickly, for example to get an overal look of the events when you're playing competitions.

Bring up the cheat box by pressing Ctrl+Alt+C and type in the codes exactly as they are here, including capitals.

Cheat code What does it do?
Ambrosia Victory: next month you go to the next episode
Bowvine and Arrow Towers shoot cows instead of arrows
Cheese Puff Diary workers will dance in cheese suits
Delian Treasury Add an extra 1000 Drachmas to your books (up to 15,000 dr)
Fireballs from Heaven Click somewhere and a fireball will come from heaven to destroy everything on that tile
Poseidon only
Mammaldrome The horses running in a completed hippodrome change into a boar, a bull, a wolf and a deer, including sound effects

The next one isn't really a cheat, but more a trick:
With the sidepanel-trick you can get free roads, parks and clear: drag the mouse cursor over one of the tabs on the panel, release the mouse-button and the road/park will be built without a cost to you.