Not only are we required to assist someone with unloading his animal (or himself), we are obligated to assist with loading in the first place. There is an important difference between the mitzvos of loading and unloading: one can expect to be paid for his help in loading but he must help to unload for free. (See Talmud Baba 32a for a full discussion of this topic.)
The reason is what we have said about unloading: helping others reinforces positive traits. Being paid in this case doesn’t contradict that. Unloading is more urgent – the animal is in pain and the owner can incur a loss. This service we must provide for free. Loading is merely for the owner’s convenience. We have to offer our help but we can expect to be compensated for our time and effort.
This mitzvah applies in all times and places. It is discussed in the Talmud in tractate Baba Metzia (32a-33a) and codified in the Shulchan Aruch in Choshen Mishpat 272. This mitzvah is #203 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #71 of the 77 positive mitzvos that can be fulfilled today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.