Side trip from my regular posts on organizing your work space and taking it with you: tools that you didn't know you needed.
Most of the tools in the toolkit are obvious- the soldering iron, the tweezers, the "helping hand", etc. There are a few items that are in my toolbox (or are always close at hand) that I use constantly but somehow never make the lists I've seen for equipping a bench.
1. Cyanoacrylate adhesive- especially the brush-in-bottle "Krazy Glue" brand that I highlighted in my tool kit post. Useful for "dead-bug" assembly, reattaching lifted pads, and temporarily holding things in place while you work on them (I know many CNC machinists who use CA to hold their workpieces down while they are in process.
2. Hot glue gun- super useful for low-cost ruggedizing, strain relief, conformal coating and mounting PCBs. Nothing fancy- a standard low-temperature hobby gun will work fine. In fact, the high temp type take a little too long to cure for my taste, and tend to be too runny to boot. A few globs of hot glue will transfer the strain from the solder joint on a wire to, well, the glue gob; if you push a PCB against a surface and squirt a little glue through some available mounting holes, you get top-notch semi-permanent mounting, right where you need it.
3. X-acto knife- best tool ever for removing the outer jacket from a multiconductor cable. By bending the cable to a sharp 180° angle and lightly scoring the outer jacket, you can easily cut through only the jacket, leaving the conductors (or foil/braided shield) intact. Also useful in hacking (cutting traces and scraping off soldermask to create a new "pad") and rework (if the board is more important than the IC, the best way to remove a SMT IC is to cut the pins off at the package with an X-acto).
4. Scotchbrite pad/steel wool- cheap phenolic protoboards tend to be unplated, so the copper finish gets oxidized. You can pour a bucket of flux over the board before you start working OR you can rub it down with an abrasive pad of your choice. Scotchbrite and steel wool both work wonders. They can be used on old component leads, too, but that's a little harder.
5. Dental pick- good for lifting leads while you have the solder melted, if you need to rework a fine-pitch SMT IC. For larger scale stuff, good for maintaining pressure on a component while you melt away the solder, or for picking off questionable stuff on the board (is it a glob of solder or something else?)
6. Magnifier- I use a 3x for reading part markings and a 10x for doing board inspection.
7. Flashlight- pairs well with the previous item. It's also handy to be able to readily direct light under components without having to rotate the whole PCB.
8. Your nose- long a favorite tool of mine, this one would've been left off this list if not for being mentioned in Todd Harrison's excellent power supply troubleshooting blog posts. I daresay not many people who've spent any time working with electronics DON'T know what the magic smoke smells like; that smell will linger long after the heat is gone, and will often be present even if no damage is visible. Sniffing around on a board (UNPOWERED) can frequently alert you to a dead or damage component, or at least the region of the board that component is in.
9. Your fingers- a non-contact IR thermometer works well, too, but for sheer cheapness and immediate availability, nothing beats the fingertips for detecting unreasonably hot components.. NB NB NB GREAT CAUTION IS REQUIRED HERE. Do not probe circuits under power with your fingertips if there is a chance of them containing high voltages (above 24-30V).