A fairly common problem I see people come across is their edge density. In one part of a mesh you may need more edges if it's a wider/larger area, but then higher up it may get skinnier and you'll not need all of those edges anymore! Here are a few ways to minimise the edge density whilst keeping your mesh clean and all quads (4-sided polygons) (Fig.01).
Okay, you should know this already, but if you don't: Cut is your friend (Fig.02)!
To keep things in quads, we'll be removing edges in pairs. Pick two edges you want to get rid of and connect between them (Fig.03).
Connect the vertices from the corners and remove the edges (Fig.04).
Need to remove another pair of edges? Do it all again! (Fig.05)
And when you're done, you can smooth things out a bit by moving edges and verts around (Fig.06).
Well, that work has reduced the edges a lot, but it doesn't really look all that great ... So let's try it again - the exact same thing, but different location and order (Fig.07).
This time, let's put the long one above, and the shorter one directly below it (Fig.08).
Remove the edges (make sure you are removing isolated vertices, too). A quick and easy way to do this is to select the edge and then hit Ctrl + Backspace. It will remove the edge as well as any isolated verts it leaves behind (Fig.09). This one rounds out really nicely (Fig.10)!
This is also really good geometry for lumps and bumps, and works well for clothing folds, knees, etc. (Fig.11) But what if I don't want to remove two edges - just one? (Fig.12)
To keep things all quads, you will always be dealing in pairs, but they don't always have to be parallel. You can remove an edge vertically and add one horizontally. This works nicely if you need to add detail in one direction but need to remove an edge row in another direction (Fig.13).
Remove one row, add another, and then connect the two with two edges inside a single face (Fig.14).
Then connect the verts between edges and you've got 3 quads (Fig.15).
That's it! I hope this will be helpful for some.