Because of the nature of the British government institutions in the 18th century, it's difficult to pinpoint exactly what can be credited (or blamed) as a direct effect of George III himself rather than Parliament and his ministers, both of which had gained significant powers since the Glorious Revolution (1688-9). Certainly, George III's very long reign (1760 - 1820) saw Britain rise from a middle-tier power to a global one, with huge conquests in Canada and India, as well as victory in the Napoleonic Wars, but much of that was because of competent ministers, a supportive Parliament, and a skilled army and navy. That said, George III did still have some tangible impact, such as abandoning the tradition of focusing on defending Hanover against the French - this 'British-first' attitude made George III popular with the common people, who hated that the previous Hanoverians had subordinated Britain's interests to that of Hanover's during wartime. George was also very popular because of his personality in general - he was a quiet, dignified and kind-hearted man that preferred spending time with his family at home rather than partying in grand palaces. He aimed to set a good example of decent, moral behaviour, and he achieved it - he very rarely drank, he never took mistresses, and quite rare for the era he actually spent a lot of recreational time with his children rather than handing them off to carers all the time. All of this made him extremely popular with the common people, and he would regularly be cheered by hundreds when his carriage rode through London or anywhere else in Britain.

His reputation among the upper classes was much more mixed - he was unpopular with the Whigs because he always sided with the Tories in Parliament, and was sometimes very meddlesome, and he showed little interest in the grand socialising occasions expected of a king, and thus he was seen as somewhat remote by other nobles and aristocrats, and he didn't hand out excessive gifts or patronage like his forebears had done. That said, this may have been a blessing in disguise, since when the French Revolution broke out and revolutionary fervour was high in Britain as well, it was George's immense popularity with the lower classes that ensured his reign and dynasty were secure when many others were being toppled over Europe or on the verge of being toppled. Some historians have even asserted that George III was the most popular and beloved British monarch until George VI, a century and a half later. It's a shame that the American War of Independence and George III's antagonistic and villainous (from the Americans' perspective) role in it has overshadowed the rest of his long reign, since he was otherwise a deeply moral, kind-hearted and honest man, a striking contrast to many of his predecessors and successors.

Source: The Strangest Family: The Private Lives of George III, Queen Charlotte and the Hanoverians by Janice Hadlow