Most LED bulbs have a maximum of around 12 watts, so they can easily fit into 60w maximum fixtures.
However, three key things to note:
#1. Failure. Despite the fact that 90% of the energy goes to light, and only 10% to heat, the most common reason for LED failure (i.e. early burn out) is poor heat management. This means making sure that there is sufficient space around the bulbs to allow them to stay relatively cool, and leads into my next point.
#2. Buy the best quality LED you can. LEDs are without a doubt the future of lighting (minimal energy, better light quality, unreal durability, etc.); however, the majority of LED products still aren't that great. Thus, don't buy the cheapest ones, always invest in at least the mid-price, if not the highest price option. After all they should last 20-25 years, so it is worth paying a little more to make sure they last that long.
I am not sure if I am allowed to say this, but Cree makes the best LED bulbs, Pharox are great, and Halo and Osram-Sylvania have some great options.
Also, it is important to look at the manufacturer warranty.
And it is critical to pay attention to the "color temperature", which is rated in degree Kelvin. Anything less than 3,000 Kelvin will be a nice warm light (2,700K is the most common favorite) and anything above that will be relatively blue in color.
#3. Check with an electrician. I would highly recommend consulting an electrician with deep experience in LED lighting to help with product selection as well as making sure that your existing wiring infrastructure will work well with LEDs.
I have had some challenging experiences with getting LEDs to work well with knob-and-tube wiring.
For more information:
Read "How do you select LEDs since we are not used to thinking in lumens?" a Q&A answered by David Bergman.