I have a light fixture that lists the maximum bulb wattage as 60W. Right now, I have a standard incandescent bulb in place. Since there is only one light in the room, a single bulb is not bright enough. Can I safely switch to CFLs or LEDs with a greater Lumen output than the standard 60 incandescent as long as I don't go over the 60W draw?
Yes. The more efficient bulb will also produce less heat, so it should be fine. The only concern is that if there is a dimmer you need a dimmable bulb, and if there is a touch switch or other circuit that was powering itself via a trickle current thru the bulb that may not work -- but neither it nor the bulb will be harmed by the experiment, so go for it.