Depending on your power supply, lots. The cheap (<$2) buck/boost converters I use on my layout are rated at 3 amps. I would not load them past about 80%, so let's say 2.4 amps. The LEDs I use draw between 5 and 20 milliamps (ma) apiece. Let's use a number on the high end, 20 ma, for the sake of discussion. 2.4 / .020 = 120. You can do the math for different LEDs and for converters that have different output ratings. The converters are so inexpensive that you might want to use several to spread out the load and remove a single point of failure.
LED lighting has truly revolutionized layout lighting. My prior layout was all incandescent, and I had to add a small cooling fan to my vintage KW transformer to keep it from cycling the breaker during long operating sessions. Now that transformer doesn't even break a sweat. My single Woodland Scenics wall wart at 1000 ma has enough capacity to power all 8 of my JustPlug structures plus all of my street lighting with capacity to spare.
