1. The story is about individual freedom. At the beginning, Rip wants to be free to converse with his neighbors and spend time fishing and hunting, but his wife is always nagging him to work on their farm. By the end of the story, Rip's wife is dead and Rip is able to enjoy being free of her tyranny.
2. Nature plays an important role in the story. Rip falls asleep in the middle of a clearing in the forest. This event is what frees him from the tyranny of everyday life because when he awakens, many of the things which bound him are either gone or dead.
3. The supernatural also plays a large role in the story. Evidently, it is the men of explorer Henry Hudson who lure Rip into the hollow of the forest. These men have supposedly been dead a long time, and they never speak to Rip. However, they do motion to him to drink from their liquor and that causes him to fall asleep for 20 years. The supernatural plays a large role in many romantic stories and Rip's story would be impossible unless something supernatural occurs to make it possible for him to sleep for 20 years and survive.
As noted by the Encyclopedia Britannica:
"Romanticism emphasized the individual, the subjective, the irrational, the imaginative, the personal, the spontaneous, the emotional, the visionary, and the transcendental."
Romantic thinkers often showed "a deepened appreciation of the beauties of nature" as well as "a general exaltation of emotion over reason and of the senses over intellect." They also were interested in folklore, ethnic cultural origins, and the supernatural.
The previous answer addresses some of these elements in Rip Van Winkle. Here are some others.
An interest in folklore and ethnic cultural origins
The story begins in a setting that was historic and nostalgic for Irving's contemporary audience. Whereas the story was published in 1819, Rip appears to start his adventure some time before the conclusion of the Revolutionary War, in a small, Dutch village in the Catskill Mountains. And the plot is reminiscent of several folktales, including Peter Klaus, the German folk tale that is believed to have been Irving's inspiration.
In addition, there are elements within the story that represent old cultural traditions even to Rip. When he leaves home, Rip encounters a strange little man dressed in the "antique Dutch fashion." He introduces Rip to a group of similar throw-backs, and we are told that the "whole group reminded Rip of the figures in an old Flemish painting." At the end of the story, their status as creatures from folk stories is confirmed:
"He assured the company that it was a fact, handed down from his ancestor the historian, that the Catskill Mountains had always been haunted by strange beings."
The importance of personal feelings, sensory experience, and spontaneity
Rip has "a strong dislike of all kinds of profitable labor," but he nonetheless spends long hours hunting and fishing. He appears to be motivated by the sensory enjoyment of these activities, not economics, and his efforts are highly inefficient, as when he would "sit on a wet rock, with a rod as long and heavy as a lance, and fish all day without a murmur, even though he should not be encouraged by a single nibble."
This brings him into conflict with his wife, who represents are more practical, materialistic point of view.
"If left to himself, he would have whistled life away in perfect contentment; but his wife kept continually dinning in his ear about his idleness, his carelessness, and the ruin he was bringing on his family."
Note that this isn't merely a question of hating work. It's also a reflection of Rip's preference for letting the intuition take over. When he goes on his walk, he does so without a conscious sense of where he was going:
"In a long ramble of the kind on a fine autumnal day, Rip had unconsciously scrambled to one of the highest parts of the Catskill Mountains."
This is spontaneity, not rational calculation.