I'm pretty tired of trying to repeatedly reference video tutorials for Blender stuff, so I'd like to start taking notes and posting them for my own reference! Maybe they'll be useful for someone else too.
This post is loosely referenced from this video.
5 to 3 Edge Loops

We're starting with 5 edge loops that we'd like to reduce down to 3. We'll need one perpendicular edge loop to work with.
On the edge where you'll be reducing the number of edge loops, select the center edge. Move it inward toward the higher-density region. You can see this forms a trapezoidal negative space- select the four vertices that border this trapezoid and create a new face. Now you have three edges that you can extrude out. You can adjust the size so the new faces end up an even width.
3 to 1 Edge Loops

This follows the same steps as the previous example.
4 to 2 edge loops

On the edge where you'd like to reduce the number of edge loops, move the two center edges inward and extrude out the single vertex between them. Make two new faces on either side using this new center vertex and extrude those out into your lower-density region.
Applied

I intended to make some sort of little homunculus approximating an arm attached to a torso. What I made, by accident, is a very bad Geodude.
Odds to evens?
Trying to connect odd numbers of edge loops to even ones or vice versa gets kind of ugly! You can do it, but you'll end up with something at least a little weird and asymmetrical.
Misc Notes
If you're working on an existing model to clean up edge loops you probably won't actually be extruding, etc! You can just slide the edges around instead and apply cuts as appropriate, dissolve edges, etc. (Did you know about the connect vertex path tool? If you're making straight cuts across connected surfaces, it's probably a faster and easier option than the Knife tool.)
This post is loosely referenced from this video.
5 to 3 Edge Loops

We're starting with 5 edge loops that we'd like to reduce down to 3. We'll need one perpendicular edge loop to work with.
On the edge where you'll be reducing the number of edge loops, select the center edge. Move it inward toward the higher-density region. You can see this forms a trapezoidal negative space- select the four vertices that border this trapezoid and create a new face. Now you have three edges that you can extrude out. You can adjust the size so the new faces end up an even width.
3 to 1 Edge Loops

This follows the same steps as the previous example.
4 to 2 edge loops

On the edge where you'd like to reduce the number of edge loops, move the two center edges inward and extrude out the single vertex between them. Make two new faces on either side using this new center vertex and extrude those out into your lower-density region.
Applied

I intended to make some sort of little homunculus approximating an arm attached to a torso. What I made, by accident, is a very bad Geodude.
Odds to evens?
Trying to connect odd numbers of edge loops to even ones or vice versa gets kind of ugly! You can do it, but you'll end up with something at least a little weird and asymmetrical.
Misc Notes
If you're working on an existing model to clean up edge loops you probably won't actually be extruding, etc! You can just slide the edges around instead and apply cuts as appropriate, dissolve edges, etc. (Did you know about the connect vertex path tool? If you're making straight cuts across connected surfaces, it's probably a faster and easier option than the Knife tool.)