Can I replace a 60 watt incandescent light bulb with a fluorescent or LED bulb that puts out more light than the incandescent?

This is probably a stupid question…please be kind. :)

Most modern lamps are labeled with something like “60 watt incandescent or 13 watt fluorescent, maximum”, since they are equivalents. But if I want more light than a standard 60 watt bulb puts out, can I use an alternative bulb that is equivalent to a 75 or 100 watt incandescent? Such a bulb would likely be higher than 13 watts, but it would still be well under the 60 watt upper limit for an incandescent. Is there some danger involved in doing this?

Bonus question: are there any lightweight LED bulbs with standard bases available? I really prefer the quality of the light from ‘daylight’ LEDs, but they’re too heavy for my adjustable task/desk lamps.