Something I learned from watching Rioforce's stuff: make it cinematic. The common thing for brickfilmers to do is get a couple lamps and light the whole scene. That's fine, but direct light and single source light is unique and, if done right, looks great. Contrast is one that can improve the quality of a scene. Experiment and think of unique but fitting ways to light your scene.

Lighting goes a very, very long way in setting the mood and tone of the scene. You'll want to figure out what setting you want first, then figure out what kind of lighting will complement that. There's no set formula or 'one size fits all' solution. It involves a lot of trial and error, but over time, you will learn what you like, and begin to develop your own unique style.

I usually have 2-3 basic desk lamps pointed right at the set from different angles. (Like this)
But for And Men Loved Darkness the outdoors shots generally used one lamp, (This.)
with the other details handled by a ton of LEDs. (This.)
I've also used Christmas lights on occasion. (Here)

It's not so much what you use, as how you use it. As my classic example of that, observe that these two frames, so far as I can remember, by the same number, and possibly even the exact same lamps. (Here and Here)

These's one thing I've learned recently that has really help with lighting up faces well. You need to reflect the light onto the minifig's face by using a bit of white paper, or even a larger white tile plate. You set that on the ground of your set, a few studs from his/her feet, then angle it until the light from the lamp is bouncing into the figure's face.

Unlike Squid, I very rarely bounce lighting on a larger scale. I don't use gels or diffusers. (Though I'd love to get some someday.) My lighting set-ups are very direct, and depending on the feel I want, pretty simple too.

Feel free to scroll through my Flickr stream for ideas, though I don't have many that show the lighting set-up as a whole.

As for films and examples:
Don't Blink was a huge inspiration for me.
ForlornCreature's Lego Minecraft films have some great lighting, and here's some behind the scenes for those.
Squid got me into the whole mini-LED thing, so check out some of his films for some more great lighting.
And SlothPaladin has done a great job recently, (particularly on this) though he also has a lot more specialized equipment than the average brickfilmer.

Also, find all the behind the scenes videos and pictures you can. Some people don't put out much, but it's always helpful to see how they do it. THACumentaries are a good source for quick and simple solutions to problems, but you'll have to wade through some fluff and silliness to get to the profitable stuff.

I think I have achieved the best lighting I can do for now without a third lamp, having the second "lamp" be a flashlight. Surprisingly enough, I can light in some dark areas very well with the flashlight; it being so bright and all