D&D adventures in general.
Then hell yeah.
Traditionally random encounters are used to keep the adventurers, and by extension the game, moving along and to present a tactical and resource management challenge; while they play that role in the games I run as well, I use random encounters more specifically as
in media res moments to make a location, or the game-world generally, feel like it exists independently of the adventurers.
Frex, say the adventurers are visiting a chateau; a random encounter could be guards patrolling the halls, a rake sneaking into or out of his mistress' chamber, the steward angrily discussing bills with the head cook, and so on.
In
our Flashing Blades game, the adventurers spotted a couple, poorly disguised as merchants, in a seedy gambling hell. They also noted that a group of cutthroats apparently saw through the disguises as well. Anticipating an attempt to waylay the couple, the adventurers followed the disguised pair into the night and broke up the bravos' ambush. One of the pair was wounded, and the other, claiming to be a duchess, demanded that the adventurers help sneak the couple into the Louvre. Disguises were readied, guards bluffed - barely - and the couple was smuggled into the palace. Meanwhile one captured bravo managed to escape, and another was murdered by the adventurers, his throat cut and his body slipped into the cold dark waters of the Seine.
The next night found the adventurers trying to find the leader of the gang, first tracking down his girlfriend, a cheap prostitute, and attempting to intimidate her into giving up his whereabouts. When that failed, they followed her into a Carmelite abbey, but decided to leave when confronted by the abbot - the abbot was also a random encounter, by the way.
As written in my notes, the random encounter was, "The duchesse de Chevreuse and Lord Holland, disguised as merchants, go slumming in a seedy tavern. Cutthroats led by Guilbert Le Pendu see through their disguises and plan to ambush the couple when they leave." Everything that followed was simply a reaction to what the adventurers chose to do.