How to Create Excellent Character Topology with a Handy Trick
Bad loops are a common issue when retopologizing characters. Topology that disrupts the flow makes the model harder to work with or animate. This tip works in any 3D software, like Maya, 3ds Max and Blender - and it's a core part of my character workflow.
A Simple Trick for Redirecting Loops
The model below is in a decent spot in terms of the loops, but I want to redirect the selected loops so that there's a clean loop around the nasolabial fold. This makes rigging the model a lot easier, and it will deform better.

A reliable way to change these loops is to look for patterns in your topology and adjust vertices until you form smooth loops.
Start by forcing the vertices you already have into the flow you want. In this case, I'm forcefully directing them around the nasolabial fold.


Merging vertices helps define new edges, but also creates a huge mess. This is a part of the process however, can can easily be cleaned up.
Creating temporarily messy topo is a part of the process. Once you spot the loops you want your model to have, connect the verts, delete additional edges and clean it up. The annotation on top of the image below is what I want to do with the topo from here. If you get stuck when retopoing, drawing on top with a tool like Epic Pen can be really helpful.

Once you know what you want, it's a matter of connecting it up.


Additional Techniques for a Cleaner Mesh
Refining edge loops is easier if you isolate the affected areas. Deleting polygons provides a blank canvas for reorganizing your topology. The Edit Edge Flow feature in Maya (Edge Flow Addon in Blender) makes the loops smoother. Here's the final result after relaxing the loops and using Edit Edge Flow to space the loops out.

Cut the Loops and Be Fearless
Redirecting loops takes a bit of practice. First, you'll need to know which loops you want in your model, and next you need to be pretty comfortable with old-school poly-modelling. But once you become comfortable with the process, you'll be able to very quickly fix your models and make excellent topology in no time.