Harm
Hare
Hate
Hats
Rats
Rams
Rims
Aims
Arms

Change "slow" to "cube".

Flow
Flaw
Flat
Feat
Felt
Fell
Fall
Pall
Pale
Pate
Cate <-- archaic; a choice food, delicacy
Cute
Cube

Change "sway" to "ways".

Sway
Swat
Seat
Seas
Sets
Wets
Weds
Wads
Ways

Change "star" to "dust".

Star
Sear
Seas
Leas
Less
Loss
Doss
Dost
Dust

Change "axis" to "evil".

Axis
Axes
Aces
Aced
Acid
Amid
Amir (variant spelling of "emir")
Emir (a Muslim, usually Arab, military commander or local chief)
Emil (had to cheat and use a proper name - "Emil" is a boy's name in Germany)
Evil

Change "flow" to "cape".

(Sorry I keep giving you impossible ones, Erlian! Usually I check on this site to make sure they're doable, but it was down for a while.)

Flow
Flop
Clop
Coop
Corp
Core
Care
Cape

Change "ties" to "shoe".

Ties
Tees
Teem
Seem
Seam
Spam
Spat
Spot
Shot
Shoe

Change "late" to "flat".

Late
Lats
Lets
Less
Lest
Fest
Feat
Flat

Change "cars" to "sped".

Cars
Card
Bard
Band
Sand
Send
Seed
Sped

Change "plug" to "gulp".

Plug
Plum
Slum
Slim
Slit
Slot
Soot
Root
Roof
Goof
Golf
Gulp

Change "Stay" to "Well"

Stay
Star
Sear
Seal
Weal
Well

Change "lamb" to "alms".

Lamb
Lame
Lane
Land
Lend
Send
Seed
Sped
Aped
Apes
Ales
Alms

Change "hard" to "easy".

Hard
Bard
Bare
Base
Ease

Change "yarn" to "knit".

Yarn
Barn
Born
Boon
Boot
Blot
Blow
Slow
Snow
Know
Knot
Knit

Change "fast" to "show".

Fast
Mast
Most
Moot
Soot
Shot
Show

Change "oats" to "meal".