2x2x2_method: color-neutral Layer-by-Layer, Ortega or freestyle depending on the scramble.
2x2x2_reason_for_method: Color-neutral because you get easier starts, Layer-by-Layer because chances of 1 look last layer are high, Ortega because it's only 3 logical algorithms to learn and gives nice short solutions, freestyle because sometimes I just see a FMC solution during inspection
3x3x3_method: white cross, 3 corners, 4 edges, last corner (my keyhole variation), optional edge-control, 2 look OLL, 2 look PLL
3x3x3_reason_for_method: Easy to learn after a beginners method. To busy/lazy to learn full OLL/PLL, still faster for me than CFOP F2L
4x4x4_method: 1st center, opposite center, 3rd center, adjacent center, last two centers, 2-at-a-time edge-pairing, finish like 3x3x3. For OLL-parity I always do a double-parity-fix I found myself.
4x4x4_reason_for_method: By far the fastest method in the world and entirely intuitive
5x5x5_method: Centers like 4x4x4 order using 3+3+3 lines or spiraling, edges with the absolutely brilliant AVG method

, finish like 3x3x3
5x5x5_reason_for_method: Also the fastest method in the world and also entirely intuitive (except for a faster edge-parity-fix I learned)
6x6x6_and_bigger_method: Centers like 5x5x5, Edges like 5x5x5 working inside-out, finish like 3x3x3
6x6x6_and_bigger_reason_for_method: By now you should have figured out that I like intuitive, yet fast.
Square-1_method: A=(1,0)/(-1,-1)/(0,1) and B=/(3,0)/(-3,-3)/(0,3)/ + a parity fix (nerdsparadise)
Square-1_reason_for_method: Did I ever mention intuitive, yet (reasonably) fast?
FMC_method: Solve as many pieces as possible in as few moves as possible. Add pre-moves and in-between moves to solve more pieces. Use insertions to fix all those nasty pieces that didn't get solved before
FMC_reason_for_method: Doesn't require any algorithms and gives great results
Megaminx: I suck