Well, as far as non-tripod stuff goes, How to Not Rob a Bank is composed almost entirely of shots where I just slapped the camera onto the set, which usually situates it pointing right at the characters.  If ever I needed a slightly different angle, I would put LEGO pieces around it to tilt it up or down, and sometimes side to side.

However, sometime about half way through filming Vladimir Vango, I discovered my family's old tripod, although only a small tripod.  So I put some stuff under my set at the time and raised it up so that it would be level with the tripod.  Using the hinges on it, I was able to do pans and other motions like I'd never been able to do before.

Although, it is rather old, and I don't know what sort of brand it is.  It's  a bit uneven, and slightly shaky, but if you don't touch it much it works okay enough.  It probably wouldn't be a good idea to get this exact tripod, but I do think having a tripod like it of a similar size and shape would be nice.  I've also been wanting to get one.

This is what it looks like:

The main reason I like this relatively small size is that it's rather easy to build a dolly machine around as depicted here in this picture so I can still used the dolly to push the camera along whilst I can get more precise angles with the tripod (and by that I mean slant the camera excessively).
If anyone hasn't yet seen it and would like to, here's my camera motion video in which I put a bit more detail about the dolly rig: http://youtu.be/RWACQUVGBss

The disadvantage of this is that you'll have to have your set elevated particularly high above the base of the dolly so that the set and camera are level.

I'm currently doing this by having a smaller piece of furniture next to me table like this with the dolly and tripod on that:

If you look closely at the dolly you can see I've set it a bit lower than I actually need to but stacked some bricks under the tripod to elevate it to compensate, this way I can reduce the stack of bricks and easily lower it for an especially low angle on the subject.  Or I could stack the bricks higher for a higher angle.  And though it takes some doing, the white metal shelf I use for this can also have its height adjusted to be even lower for if I'm filming a set which is significantly less tall.

Overall, I really like dollies, and a tripod of this size is really good for that.  However, the tripod itself is not as good as it could be, so I'd suggest looking for something of a similar size.

I also recently got a big tripod that can go one the floor, but because of that it's much too big for my dolly.  I'm planning to use it for shots that are really high up, but, as of yet, I haven't animated anything for a film with it, although I did use it to take a few pictures of the town.

I've stopped using a tripod. During production for Unhealthy Foods, I kept getting really bad camera shakes and I had nothing to do with them. I never bumped the set or the camera. But then AquaMorph told me on the chat one day that it was because the tripod was on carpet. He said to add a weight to the tripod. I tried that, but it made it worse. So then I just placed the camera on the set above two pieces of clay. That seemed to solve all my problems. Plus, I can get closer up.

TwoGuysBrickfilms Youtube Channel

Thanks for the responses, guys. It seems like tripods aren't a major point of contention among brickfilmers. I suppose not everyone even uses them, and most people aren't trying to execute detailed camera moves with them.

Massive bump.

I ended up getting a new tripod in early 2016.

I use the Bogen 3001 tripod legs (I took off the stock head) and a Manfrotto 410 tripod head.

(dog not included)

I also have a Neewer macro geared focusing rail which I use for dolly and pan shots. It mounts atop my Manfrotto tripod head and provides good movement. It's slightly wobbly with both rails attached, but they come apart so you can have one at a time if you wish.

I'd be interested to revive this topic and hear what everyone else uses! Tripod discussions are three times as interesting than monopod discussions.

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"Whatever you do, do all to the glory of God." - 1 Corinthians 10:31b

I'm using a DSLR so usually there isn't room on my table for the camera.   For this reason I do use a tripod.  I'm using a Manfroto video tripod: http://amzn.to/2oyI1UQ
It has really good control and mobility.  The only issue is that you have to make sure it is tight before you start filming or it can droop with a heavy camera.