I often get comments like “you *should* remove that triangle,” when I can give at least five good reasons why that person is wrong.  Newbs just have it ingrained in their heads that EVERYTHING MUST BE QUADS.  It’s not their fault, though; they’re just not taught WHY triangles are SOMETIMES bad. Especially in the case of low-poly game models, triangles are GOOD! For those who don’t realize it, quads are merely two triangles glued together, and the quad is just split differently depending on how it’s bent or skewed. Unfortunately, quads don’t always split the way you want them to. In fact, unless you have a relatively high-poly mesh with good topology, quads rarely split the way you’d like them to.  Sometimes, it is better to decide how to split that quad ourselves.

There are two cases where triangles are bad:

1) if your model is to be subsurfed.

2) (in an un-subsurfed model) if they will disrupt the shape of your object during animation.  Basically, if they don’t go with the edge-flow (no pun intended).

If your model will not be subsurfed, and your triangles don’t interrupt the edge-flow of your model, they’re perfectly fine.

Also, if an object is static (not animated), you can use all the triangles you want on the solid surfaces, regardless of edge-flow, like so:

Observe the hideous gash in this heel due to a poorly folding quad: (whoops, sorry, Blender saved a screenshot of the “save file” window instead, and I honestly can’t figure out how to recreate the hideous gash…)

Which is nicely fixed with a couple of tris:

However, in this case, we can actually save polygons by merging those couple vertices.

Here’s another gash, but it’ll much less noticeable in-game, and has a much higher chance of straightening itself out during animation, so we’ll leave it.  Basically what I’m showing you here is that quads aren’t always good.

Here, I made use of triangles to put a crease in the palm of the hand.  I could merge the two triangles into a quad, but I want this specific crease at all times, so my BEST choice is to leave them as triangles.  Also notice the tri to the left, which I used to reduce the edge loops.  None of these tri’s will interrupt my edge-flow during animation, so they are PERFECTLY ACCEPTABLE and are in fact GOOD.

The next time someone tells you that some stray triangle should be removed, ask yourself, “Is this person a newb?” and “Does the triangle hurt my model for the use I intend?”  If all triangles were evil, we wouldn’t be given the ability to make them.  Remember that.

I hope this was helpful to some people; I just wrote it on a whim, after modeling this character:

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(Whoops, there were some typos in the Blend’s “license.” Fixed ‘em…)