I only storyboard for longer projects, or for projects where I think that the cinematography is important. I spent a week storyboarding Ozymandias before I started animating, but for stuff like Avengers Tower I didn't see the point. For brickfilming, it's really just about what you want to get out of the end result.

Live-action is another matter entirely. Setting up shots is more difficult (I find) so I like to have a detailed storyboard first. For our AS Film Studies coursework, my group and I storyboarded two separate versions of the film before deciding which of the two ways we wanted to shoot it. These things are important.

But for brickfilming, I'd say it's less important, unless it's a bigger project.

"Nothing goes down 'less I'm involved. No nuggets. No onion rings. No nothin'. A cheeseburger gets sold in the park, I want in! You got fat while we starved on the streets...now it's my turn!" -Harley Morenstein

I only story board for longer, more detailed and larger sets. Everything more simple I don't worry about to much. If there are a lot of characters, action or big sets, I story board. That way I know what I need to build and what it needs to look like before actually building it.

I've only rarely storyboarded a film on paper.
It's easier to keep things in my head, and the time-investment-to-production-benefits ratio is low enough on short Lego films to usually not be worth it.

Truthfully, I have a few ideas for certain shots in my head, but mostly just wing it throughout the filming process.
Just finding an angle that looks good and going with it seems to have worked so far, it takes less planning time, and then I don't feel forced into a preconceived mold of what needs to be done.

That being said, there are many times when storyboards are very beneficial. When communicating your vision to others, when planning big effects shots or complex sequences, longer/bigger films, Ect...

I storyboard but only when it can be done quickly.  Some people can spend weeks sketching up a board - that confuses me.  Sure, it can avoid mistakes but would it save weeks of mistakes?  I'm guessing rarely - but sometimes.

I storyboard by making stills of each camera shot I want to do - even for a short film.  I need to build a set for a storyboard - so I'll make the real set or an approximation.  I'll put figures in a meaningful position and take a still and add that to my storyboard.  It takes almost no time to make a storyboard this way, though I grant that its missing dialogue.  Even that can be added as captions or speech bubbles if you cared enough.

Strictly speaking, what I do may be a quasi-storyboard, but it forces me to think about the set, the mechanics of moving figures around the set, camera and zooms.

Sketching a storyboard for weeks?  No thanks.  Spending 45 minutes taking stills of sets with correct camera angles and arranging in sequence.  Every time!

Drawing everything is just painstaking. That's why.