The Washington Post published a basic but informative guide to repotting houseplants today. An excerpt (free login required to read online):
Don't take a plant in an eight-inch pot, say, and put it in a 12-inch one, thinking this will delay a future repotting by a few years. Too much soil will stay wet, even in a well-drained pot, and the roots will melt away. Increasing the pot diameter by one or two inches provides enough room for two to three years of additional growth.The article stated that most houseplants are safe to go outdoors "full-time" when nighttime temperatures consistently stay above 50 degrees.
A truly pot-bound character may be hard to release. Submerging the pot in water for half an hour may help, as will taking a knife and breaking the contact between the roots and the inside of the pot. Sometimes you have to cut away plastic pots or smash clay ones to free the plant without destroying it.
You will want to tease out congested roots before putting a plant into a larger pot, but a root ball that is a solid mass is another matter: It should be cut back on all sides by about one-third; then it can go back into the same pot. [Link]