I am playing Monopoly and I land on the 'Go to jail' space. The player next in line rolls, and lands on Park Place, which I own. He challenges me, and says that he doesn't have to pay rent, because I am in jail. Is this true?
Being in jail prevents you from moving. It doesn't prevent you from doing anything else.
You can buy property (at auction), trade properties, build houses and hotels, and yes, collect rent.
Unless there is a "house rule" against these moves, usually against the last one.
Being in jail only prevents you from moving, and does not prevent you from doing any other action, including collecting rent. The rules state:
Even though you are in Jail, you may buy and sell property, buy and sell houses and hotels and collect rents.
This is a very popular strategy late in the game, as the less you move, the less likely you are to land on your opponent's properties.
In addition, the rules specify that the only times you do not pay rent is when the property is mortgaged or if the property owner does not ask for rent before the next player's turn.
Not being able to collect rent is just one of many fairly common house rules.
Some house rules disqualify an owner from collecting rent while in jail. This allows reprieve for other players landing on an expensive property with houses or a hotel during the time a player is incarcerated.
While this is not an official rule, some people choose to play by this house rule.