It certainly helps to own as many properties as you can afford because each time someone lands on that property, you get paid. How much you earn depends on whether you have a set or not (cost is doubled if you have), and whether you have hotels or houses built on them (hotels on the more expensive properties can cripple an opponent).
The nature of the game is such that you'll be buying up as many properties early on in the game (as many as you dare) so that when deals start to be struck, you'll be right in there with something to offer. This is because once one player hasa set, the others need one as well, or it will be a ... monopoly for the first player. This is because once houses are built (they may be built when a set is obtained), the cost to land on these properties increases dramatically.
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Unless the other players are also collecting this high rent, the player with the original set is a heavy favourite to "hoover up" all the remaining money sloshing around with thier extra high (relatively high) rent.
Monopoly game contents :-
Game board, two dice, play money, 32 houses, 12 hotels, 11 tokens, Chance and Community Chest cards, Title Deed cards for each property.
See my Monopoly strategy guide (links to all monopoly articles are on the left hand side or at the bottom of this article), for information on deal making, the probabilities of landing on each set, trading and other tactics and tips.