I'm just getting into this game and I've built a basic coal to power plant train delivery system. I'm curious, since power plants can accept an unlimited amount of coal, is there any reason to deliver coal to multiple plants instead of delivering all the coal to one?
While there are mods available that add mechanics regulating the demand side (that means, adding limits to the amount of coal for example, that a power plant can process in a certain timespan), in vanilla OpenTTD any processing plant can process unlimited amounts of goods.
However, delivering the goods to the most distant plant will yield the maximum amount of profits, so you might need to supply more than a single one. There is an in-game chart that shows the profit per good by (days in transit vs. distance travelled), and you can see that especially coal profits a lot from large distances.
Normally, you would start building around a single plant, and connect multiple mines to that, in order to reuse existing infrastructure. Then later re-route trains to go to different power plants that have a larger distance.
As Private Pansy correctly mentions, in the late game you need to optimize your track layout in order to get it more efficient. That means removing any "wait until fully loaded" orders and usually packing your tracks with the maximum amount of trains affordable. This is less important for coal, but highly important for other goods (say, fruits in the desert setting).
There's one additional reason to use two power plants, and that is making more money with each train, to increase their effective ROI ratio. With the default trainset, refits are typically expensive or not possible, so you would have trains hauling empty loads back in a simple setup. With two plants, you can haul coal 'both ways'.
Suppose you identify two pairs of power plant and coal mine, close together, with both pairs far apart. You could build two small train lines, but since you're paid 'by the square', it can be far more lucrative to have your train line go:
Coal mine #1 ----> Plant #1 -> Coal mine #2 ----> Plant #2 ->
where longer arrows represent greater distances. You can get (almost) twice the income over a simple one-way empty, one-way full connection. Almost, since you will probably need a small distance between the Plant and the next Mine, and since full trains are heavier and accellerate slower.
By the way, this is a great way to jumpstart your company in openTTD, and typically regarded as the optimal opening move on most maps/settings. Here's a link to a more in-depth tutorial.