To remove residues of tape-glue, just use other tape: Stick it on then pull it off until the tape has removed all residues.

Use crepe tape on wood before cutting it. 1) The saw blade won't frazzle the wood then, as the tape holds the woodfiber together. 2) You can draw your cutting line on the tape.

Always use more insulation tape on the handle bar strap of your racing bike than needed. This way you always have some tape with you.
Wrap duck-tape around a pen to have some portable with you (plus the pen itself :)

Bondage-Tape is not only good for fixing your partner. It is like strong cling wrap which sticks to itself without any glue at all. There are other reusable-tapes which work on the same principle. Think outside the box.

Use powerstrip if your surface is not flat (as it is fluffy and squishes).
There is even tape which is supposed to work under water (flex tape) - haven't tested yet.

Use clear tape (Tesa) with superglue to make fingerprints visible.

Always de-grease your suffices at least with detergent, better use brake cleaner.