"Some say the world will end in fire,
Some say in ice." ("Fire and Ice")
A very literal reading of Robert Frost's poem would suggest that the speaker of the poem is, in fact, discussing the end of the world. The speaker in Frost's poem favors ice as the de facto killer of our planet, and planet Earth has had cold stages, or ice ages, in the past.
As for the sun 'bursting,' well, that would not really happen just unexpectedly. The sun is a star, and even stars have a 'life cycle.' Our sun would turn into a red giant first (which would take millions of years); if that happened, it would impact our temperature on earth, possibly resulting in another ice age.
As for end of the world poems, I like this T.S. Eliot's view from his poem "Hollow Men:"
"This is the way the world ends
Not with a bang but a whimper."