classic/classical That was classic! (It was typical of the genre/person.) Classical architecture is modelled on the styles of Ancient Greece and Rome.
compare with/to (You can’t compare apples with oranges/Shall I compare thee to a summer’s day?)
diaresis, diuresis
forgo/forego (deny yourself/precede)
further/farther (quantity/distance)
gourmet/gourmand (discriminating epicure/pig)
grill/grille They both mean a metal grid, but a grill is a thing you put over embers for cooking purposes, and a grille is a barrier over a convent window, or a car radiator.
historic/historical (worthy to go down in history/from an earlier era)
rise/arise When smoke ascends it rises. When things arise they occur.
shall/will (I will do what I like. (I intend to…) I shall do what I like. (prediction) You will come tomorrow. (prediction) You /shall/ come tomorrow! (order))
shorn/sheared They must have the same root, but only sheep are sheared. People are shorn of their hair, titles or dignity.
staunch/stanch Fowler says there's a difference, but...
A Dictionary of Modern English Usage: The Classic First Edition: The First Edition (Oxford World's Classics)
straight/strait These probably have the same root. One means undeviating, the other narrow.
title/entitle If you title something you give it a name (Gone with the Wind). If you’re entitled to something you have a right to it.
veracity, voracity These have completely different roots. Veracity is truth. Voracious animals are hungry.
void/devoid
waste/wasteland (Siberian wastes/industrial wasteland)
which and , which (long explanation follows... soon)

NO, NO, NO there really is no difference in meaning between these pairs

among/amongst
complacent/complaisant
complement/compliment
country/countryside
different from/to
dispatch/despatch
due to/owing to/because of
each/every
faith/belief
feeling/emotion
hanged/hung
hmogenous, homogeneous
in/within
instinctive, instinctual
learnt/learned
older/elder
oldest/eldest
on either side/on each side
sceptic/skeptic
single and double quotes
title/entitle
triple/treble
truth/Truth
unreasoning/irrational
upon/on
which and what
while/whilst
wisdom/knowledge
within, in

Sometimes similar words are given euphemistic and pejorative meanings (one's a boo word, one's a hooray word). They're filed under Boo/Hooray Pairs. And there's more Pedantry here.