Except through inheritance, the proper answer to this question is NO.
However, there have been exceptions to this rule, for a variety of reasons. Most of them have no justification whatever.

The commonest infractions of the rule have been in the case of municipalities which have given permission to various bodies associated with the town or city to use the civic arms as a symbol. This quote from Civic Ceremonial by J F Garner (Shaw and Sons), while referring specifically to the position in English law, states the issue crisply:

“A local authority cannot authorise other persons or bodies to use their arms so granted by the crown, as this would be (strictly) a usurpation of the Royal privilege to grant arms; nor can a local authority prevent another person from using their arms by any proceedings in the ordinary courts of law.”

Garner goes on to explain how suit may be brought through the Court of Chivalry (the Earl Marshal and officers of the College of Arms sitting as a court of law) to prevent such abuse. (See this article for more detail.)
With regard to the specific issue of transferability, it is clear that a civic corporation cannot will its armorial ensigns away.

In at least one instance the Bureau of Heraldry has registered arms in contradiction of this principle, when it confirmed the use by the Wynberg Bowling Club of the arms of the Municipality of Wynberg.

The upshot of this confirmation is that Wynberg Boys’ High School is barred, by a certificate hanging in the bowling club’s clubhouse, from using the town’s arms, despite the fact that it has borne these arms (albeit in slightly altered form) as a school badge since the 19th century. By rights both institutions should bear differenced arms, and neither the plain arms of the town.

There are instances where family arms have been transferred.

In the early days of heraldry, before the kings of England and Scotland appointed Kings of Arms, a man would often take the arms of his heiress wife’s family – not as an inescutcheon of pretence or a quartering, as might have been done in later centuries, but as his own arms. (See this article and this one for explanations of these terms.)

A famous example of this is Bruce of Annandale, where the Bruce who married the heiress of Annandale took his father-in-law’s arms, abandoning his own family’s blue rampant lion on silver (more information on this connection is given in this article).

These arms were borne by Robert Bruce (*1274 †1329) until he proclaimed himself King of Scots in 1306.

(Examples of differencing of the Annandale arms by later Bruces can be seen in this article)

However this practice was largely abandoned when arms came under stricter control. Its nearest equivalent nowadays is in what is known in English law as a “name and arms clause”.

Medieval writers often made reference to a right purportedly claimed by knights who had captured a certain knight in battle, or defeated one in the tournament, to with that the captor was then entitled to the arms of the defeated knight. But no examples of this practice seem to have been recorded.

A notorious example of arms being transferred from one family to another occurred in the case of the Spencer family.

An ancestor of this house, John Spencer, was in 1504 granted arms: Azure a fess Ermine between 6 sea-mews’ heads erased Argent.

This article shows how a Tudor herald of questionable ethics (Richard Lee, Clarenceux King of Arms) acknowledged an entirely unsubstantiated link with the medieval family of Despencer, and awarded their arms (with the addition of three escallops) to the Spencers.

These arms have been borne to this day not only by the Earls Spencer (the family from which Princess Diana sprang) but (as a quartering) by their Churchill cousins, the Dukes of Marlborough.

It is interesting that when Prince William was assigned his own arms (the royal arms with a label suitably differenced), he chose to use an escallop. His brother, Prince Harry, uses three escallops. (See this page for the illustrations, as well as an image of Princess Diana’s arms.)

To conclude, an entirely ludicrous example of arms being “transferred” (in a manner of speaking) concerns a 19th-century British ambassador serving in Washington DC.

As was the custom of the time, he brought from England with him a carriage painted on the sides with his coat of arms.

The carriage was being repaired at a coachbuilder’s yard when an American customer of the coachbuilder saw the carriage and asked what image was painted on the sides.

On being told that it was the ambassador’s coat of arms, the American’s response was that it was “mighty fine” – and promptly ordered that his own coach be painted with the same image.

Several other carriage owners imitated this usurpation, and for a while the ambassador was constantly surprised (and no doubt horrified) to see his arms on other people’s coaches.

This says a great deal about ignorant aspirations, but since it was mere show-offery, it is perhaps not a serious instance of heraldic usurpation.