Bail - bale
The basic meanings of the two spellings bale and bail are separate, although they are perfect homographs. Some modern uses have come so close together that the words are spelled wrongly when used. The rule of thumb is: when improving a poor situation, use bail; but when extricating oneself totally from a bad situation, use bale. It may also be helpful to think of bail (out) as transitive, and bale (out) as intransitive. What you should NOT do is be inconsistent in their usage, as in this from a report in The Guardian: "Bailing out Wall Street's bad debts when millions of Americans can't pay their bills is like baling out a boat springing leaks while the sea is rising."
The central meaning of bail n.1 and v.1 is to do with the law and releasing prisoners for a sum of money. bail n.2 and v.2 are obsolete, to do with hoops or rings. bail n.3 and v.3 are, like "bailey" (the grassy enclosure of a castle), to do with fortification and confining animals: the v. is rare. (It gives rise to the "bail bar" of a typewriter.) bail n.4 is a cross-bar, more or less obsolete except in cricket. bail n.5 and v.4 are the meanings that are most easily confused with bale. The noun is an obsolete name for 'a bucket', and the verb, still in demand by sailors, means "to empty the water out [of a boat] by using a bucket", or indeed a bailer.
The commonest confusion is with bale v.2, which comes from bale n.3. The noun means a bundle or wrapped parcel of substances (hay, cloth etc), and the verb in at least one sense means 'to throw [such] a bundle out [e.g. of a trapdoor]'. This appears to be why we use the image of a great bundle falling to describe an airman parachuting or baling out of an aeroplane. (Other meanings of bale as a n. are more or less obsolete, being adj. and n.1 "evil"; n.2 "a bonfire"; v.2 an obsolete 'to dance'; and v.3 "an erroneous spelling of bail v. 4" (OED, from which all this information is derived, and whose numbering system has been followed.)
Be careful, then, when emptying boats of water, or similar figurative meanings, to use bail; but when emptying aeroplanes of people to use bale.
Bale (ill, pack) and bail (bis)form one of the sets of homophones listed by the then Poet Laureate Robert Bridges.
(For more, see Bridges homophones). AWE has a category listing our articles on each of these.