There are a few Blender tools that I consider indispensable, but that are not included as part of the default configuration. Note that the uses described below are not intended to be comprehensive explanations, but rather windows into how I use them in my workflow. To really understand the full depth available, read through the documentation of each of the tools!

In the interest of preserving these addons in a functional state as Blender goes through upgrades and in the event that the original creators decide to move on or otherwise stop maintaining them, I have set-up a GitHub repository for them here. LoopTools is not included, since it's since become part of Blender's main set of included addons.

LoopTools

LoopTools is a set of addon utilities that make dealing with contiguous edges much easier. It is included as part of Blender, but must be enabled through User Preferences > Addons. Once enabled, you can access the various tools through the Specials (w) menu.

The LoopTools suite consists of seven tools, five of which are incredibly useful and two of which are generally too idiosyncratic to be useful very often. One really important note about these tools: they do not often cooperate with modifiers, especially Subsurf and Mirror. Disable or apply your modifiers while using them, and then turn them back on or re-apply them once you've achieved the desired result.

Curve

By the far the single most useful tool in the suite, Curve arranges vertices in an object into a smooth curve, as dictated by whatever you have selected. There are two different modes of use, which you can read about at the link above, but by far the most useful is Boundary mode. In this mode, you select vertices (or edges, but I tend to prefer vertices because it affords more control) surrounding the vertices you wish to correct, activate the Curve tool, and check on Boundary in the tool options. The tool will calculate the curve implied by the vertices you have selected, and then position the vertices bound (hence the name of the mode) by those vertices on that curve. The Regular option indicates whether or not the tool should try to distrubte the bound vertices evenly, or just remain as close to their current location as possible. Here's an example of how this can be used:

In addition to the general warning that applies to all LoopTools, Curve has a few gotchas to watch out for. For one, it really pays to Split the faces in the area you're working on off before using it. Even with Boundary turned on, Curve has a penchant for affecting weird, random elements of geometry in very strange ways. Split, do your Curve stuff, Remove Doubles. In other cases, Curve will not seem to work at all. This often happens when a triangle or N-gon is involved. To get around it, again Split the section you're interested in, either exempting or including the polygon causing the problems, and change it into a quad however best suits your needs. Apply Curve, then undo (manually, not with the Undo command) whatever you did to create the quad and put the geometry back together. It's a bit tedious, but the benefits of using the Curve tool vastly outweigh the peculiarities.

Loft

Loft creates polygons that span separate edges. Rather than try to explain this in great detail, here's an example:

In situations where the number of vertices in two curves don't match, Loft will do its best to nicely triangulate down to the lower of the two from the higher. Loft can be easily confused by vertex normals, computed curve direction, and even selection order, so don't get discouraged if it doesn't work quite right all the time. First, try modifying the Twist value. Often, tweaking this to ±1 or ±2 is all that's required to fix it.

Loft also has a few more complex settings. You can specify a number of Segments, which subdivides the new geometry in the loft direction. However, you can also change the Minimum Width and and Strength. Strength of 0 creates a loft in a straight line between two curves, while making it positive or negative will bend the loft in either direction. Minimum Width will merge down smaller polygons, so as to prevent excessive geometry creation.

Loft is especially powerful when combined with Fillet (see below).

Bridge

Bridge is very similar to loft, but instead expects a pair of closed loops as inputs. This can either in any form, but the easiest and most useful is to select two groups of faces. Bridge will match the faces together to create, well, a bridge between them. Think of Bridge as a specific-case version of Loft.

Space and Relax

These two tools are so closely related that I'm lumping them together. Relax takes the given selection and reduces the apparent tension in it. It pulls every vertex in the selection just a bit closer to every other vertex. If you run it enough times, with enough iterations, you'll eventually end up with all your vertices at the same coordinate. It's particularly useful in conjunction with Curve as a means of correcting geometry along continuous sets of edges.

Space is, in some ways, the opposite. It takes the boundary region of any selection and evenly spaces out all of the bound components within that region. This is most often useful along a single continuous set of edges for making the distribution of vertices along the edge more uniform. In particular, you can play with the Influence percentage to tweak the selection by just the right amount.

EdgeTools

Similar to LoopTools, EdgeTools is a suite of smaller tools. There are only two tools in this suite that I use extensively, so I'll focus on those two. If you're curious about the others, hit up the documentation!

Extend

Sometimes, it's really useful to see where an existing edge "would be" if it were just a bit longer. Extend provides the answer. Select any edge or set of edges and activate the tool. It will create a new edge with the same direction extending from the endpoint(s) of the selected edge(s). You can choose to extend either Forward, Backward, or both. These directions are dependent on what the tool calculates as the edge direction, so are not uniform for every edge. You can also specify the Length of the new edges.

By itself, Extend has limited utility, but when coupled with other tools (Loft, Curve, and the next tool, especially) it becomes particularly powerful.

Slice

How often have you had some edges that intersected (or that could intersect with Extend) that you wanted to make properly intersect? Slice is your answer. Slice will take a plane and an edge and slice the edge with the plane. Check out the example below for how this can be used to great effect.

Fillet

This tool is not part of the standard Blender suite, but rather is a tool created by a BlenderArtists forum user zmj100. He (or she!) created a number of interesting tools, most of which I haven't actually explored in great detail yet. You can download it and the other tools from this thread.

Fillet is very straight-forward: select two edges, press the Fillet button. Any attached faces will disappear, but where you once had two edges, you'll now have a smooth curve that segues between the first and second curves with an arbitrary Distance and with an arbitrary Number of Sides. Combined with Loft, it becomes very easy to create new, smoothly-curved corners very quickly from hard-edged geometry where Blender's built-in Bevel in unsuitable.