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Useful list of things worth animating (I will continue to update). At the moment I've ordered it alphabetically by subheadings, but it might be worth me ranking the value of ideas at some point:

Elements:

Fire - (eg. campfire/indoor fire/stove/gas on the hob/house fire/etc.)
Water Flowing - (eg. pouring out a tap/river/drain/etc.)
Water Reflection - (eg. light twinkling as water moves on a pond/lake/river/etc.)
Wind Blowing - (eg. animating the effect of wind on items such as: leaves of trees/clothes/grass/etc.)

General Techniques:

Easing
Changing Dimensions of Object For Movement - (eg. body squashing when landing a jump/ball squashing when hit ground/etc.)

Humanoid Walk Cycles:

Basic Humanoid Walk Cycle - (ie. going from left to right across the screen, not at an angle).
Towards Humanoid Walk Cycle - (ie. a human facing directly at the screen and walking straight towards it)
Away Humanoid Walk Cycle - (ie. a human facing directly away from the screen and walking away from it)
Above Humanoid Walk Cycle - (top view)
Angled Humanoid Walk Cycles - (eg. looking at human from below to the left/ above to the left/ below to the right/ etc.)

Humanoid Run Cycles:

Basic Humanoid Run Cycle - (ie. going from left to right across the screen, not at an angle).
Towards Humanoid Run Cycle - (ie. a human facing directly at the screen and walking straight towards it)
Away Humanoid Run Cycle - (ie. a human facing directly away from the screen and walking away from it)
Above Humanoid Run Cycle - (top view)
Angled Humanoid Run Cycles - (eg. looking at human from below to the left/ above to the left/ below to the right/ etc.)

Humanoid Activities:

Skipping
Hopping
Leap Frog
Hand Movement (eg. hand clenching and unclenching/typing/playing piano/opening package/rolling cigarette/etc.)
Hammering a nail
Getting into bed
Getting out of bed
Putting on a shirt
Opening a door and walking through
Admiring oneself in the mirror
Taking a glance out the window
Eating a hot dog

Materials:

Metal Rod Snapping Back - (eg. a metal rod/ruler/etc. being bent then being let go, so it springs back into place)
Wood Stick Snapping Back - (eg. a wood stick/rod/ruler/etc. being bent then let go of)
Wood Stick Snapping - (eg. wood being bent until it snaps)

Objects:

Ball Bouncing - (eg. from dropped, with acceleration towards ground, deceleration away and squash upon impact).
Ball Impacts - (eg. football/soccer ball/tennis ball/squash ball/etc. being hit)

Particle Physics:

Water
Fire
Explosions
Sand