Pull-ups are required for outputs that are open-collector or open-drain outout types. The pull-up resistor is what provides the high state of the signal, because open-collector output ports, typically, can only drive a signal to ground. They can't drive a signal to +5volts. The resistor does this.

Further, the value of the pull-up resistor can be important because it dictates the rate at which a signal goes high. If you're trying to generate a signal that needs to toggle fast, a weak pull-up (too high resistance) will pull the signal high too slow, and your'e signal will flounder.

Note that some PIC pins have internal pull-ups you can enable, but they are the weak variety.