+1 for pivots. Also shadow naturals.
Everything you need to know about standard:
Waltz - Prep, 1-3 of Natural, Spin Turn, 4-6 reverse turn, whisk, chasse to close
Foxtrot - Prep, feather, reverse turn, feather finish, three step, natural weave
Tango - 2 walks, link, close promenade, corte
Other figures are buried in these basic patterns as variations in alignment, amount of turn, rise/fall, rotation, swing, sway, and/or shape.
To pick on pivots . . .
Consider the following which all derive from being able to do a good spin turn:
Back LOD into corner for spin turn and exit backing DC new LOD.
Back LOD along line of dance for spin turn and exit backing DC same LOD.
Spin turn with reverse pivot - Back LOD into corner and exit backing DC to pivot to new LOD/DC on &.
Spin turn with natural pivot ending - Back LOD along line of dance and pivot on 3 to end LOD for natural.
Syncopate from PP traveling LOD - gentleman pivots to close PP on 1, pivot on &, rise to overturn spin turn on 2, and pivot on 3.
Syncopate from spin turn - pivot on 3 of entry spin turn, pivot on 1, pivot on &, rise to overturn spin turn on 2, and pivot on 3, repeat . . .
Foxtrot version has much less rise and more travel.
Tango version has no rise and is more compact.
Quickstep version is tighter and faster with very little rise.
With each increase in difficulty, one's spin turn needs to be more precise and clean.
If one's basic spin turn is wobbly, off-balance, pops, falls on a foot, not over a foot, disconnected from frame, fails to move, not shaped properly, etc., the pivots will be worse.
Stealing from Victor Fung's DVDs @ Dancevision . . . "Believe in Basics"