Regardless of whether you're using an overland style 4x4 trailer, a traditional travel trailer, or one of the really cool new teardrop styles, power when off the grid will always be a concern.
While your vehicle will provide power and charge your trailer battery(ies) while connected, once you're parked & setup, you'll need to run your gadgets, lights, and accessories for hours or days.
Naturally one of the best investments to help manage power can come in the form of a solar setup. Once your solar system is setup & configured for your trailer, it can provide clean, free power for years to come.
Hema Maps published a great article covering Camping with Solar Power. While they voltages are different than those in North America, the concepts of amperage, watts, and capacity are still applicable to us.
If you're an Amazon customer, there are several great options for an inexpensive solar panel setup:
Goal Zero is a common brand that manufacturers a variety of solar panels & battery systems. While they're not the least expensive, their gear is well thought out and tested.
Flexible Solar Panel
For a more portable option that still provides great power, a flexible solar panel like this 60w version from PowerFilm can be a good solution.
80W Portable Solar Panel
For max power in the smallest package, this 80w hard-sided solar panel from GoPower! folds up nicely and includes a stand so you can always get max power from the sun.