Categorized by material:
I) Cloth
I) Cloth
A) Gaffers Tape, see this thread. Or Apollo Gaffer Tape.
B) Spike Tape
C) Friction Tape
II) PlasticA) Vinyl, PVC,
III) Paper1) Electrical Tape, Scotch® Super 33+
2) Color Coding Tape, Scotch® 35
3) Dance floor tape
4) Heat activated, hem tape, Stitch Witchery® (for the costumers)
B) Clear tapes, cellophane1) Gelstring Film tape
2) Packing
3) Strapping, filament tape
A) Artist's, board tape
B) Masking tape
1) Natural, High-tack
2) Blue/Purple, Low-Tack
3) Black, Negative tape
C) Drywall tape (great for single use Hang Tapes)
IV) FoilA) Aluminum uncoated, muffler tape
B) Aluminum Black, BlackTak™
V) Double-Stick, Double-sidedA) Further categorized by substrate and adhesive
VI) Specialty Tapes1) Carpet tape
2) "Snot tape"
A) Glow Tape
B) Decorative (prismatic) tape
C) Surveyor's Tape
D) Crowd Control "Police Line-Do Not Cross" tape
X) Duct, or Duck Tape. Has absolutely no reason for existence, other than bundling trash for the dumpster. Even for HVAC purposes, contractors recommend adhesive-backed foil tape.