What statements in the poem suggest that the two roads are to be understood as something more than literal paths in the woods?
This is actually a complex question because it delves into Frost's aesthetic of poetics: the question of how does he do what he does. It seems to me that we have no give-away to the non-literal meaning of the poem until the last stanza--when reading the poem with fresh eyes as one who has never encountered it before--as the early stanzas ring true of a poet waxing lyrical about a romantic walk in the woods one day. It is only when we read of "ages and ages hence" and the "sigh" and the import of "I-- / I took ..." that we begin to question the true meaning of our encounter in the woods with those "Two roads [that] diverged in a yellow wood, ...."
I shall be telling this with a sigh
Somewhere ages and ages hence: Two roads diverged in a wood, and I--
I took the one less traveled by, And that has made all the difference.
One reason for thinking that the roads in the poem are not merely literal is that the idea of travelling through woods has often been treated metaphorically in poetry. So has the idea of journeying in general (as in "The Wanderer" and "The Seafarer"). The opening of Dante's Inferno is perhaps the classic case of a speaker moving through metaphorical woods. Another reason for thinking that the roads are metaphorical is that it seems unlikely that a poem would be written about literal travel down a literal road. Poems often tend to be reflective and meditative (especially lyrical poems), and so even the title of this poem suggests that the road is figurative rather than literal. Finally, the fact that the speaker recalls his decision and continues to brood over it suggests that the decision is not merely literal. There would be little reason to ponder the decision if it were simply the choice of one literal road over another.
The speaker of Robert Frost's poem, whom some critics believe is his indecisive friend Edward Thomas since Frost himself made a statement that the poem was written about him, was known to have dwelt upon the irrevocability of decisions. As he describes the road he takes in a different manner from earlier in the poem indicates his interminable debate upon choices. With his proclivity to aggrandise one choice over the other, Thomas's perspectives alter as the poem progresses.
This narrator reminds readers of the shoppers who cannot decide upon an item of clothing. Then, when home, the shopper reflects, "Maybe I should have bought ----. That might have looked better on me, worked better for me, etc."
I agree that #3 posted a very poignant answer. The fact that Frost wrote consistently using extended metaphors provides the key to the roads existing as something more than a literal road. The fact that the symbolism of the roads less, or more, traveled is important as well given that it already exists as an image people can readily recognize.
I think the last line can be interpreted differently. Just saying that it made a difference does not necessarily mean it was a positive difference. For all we know, the man might have been lost in the woods writing the poem! I don't think that's a likely interpretation though. More likely, the roads are a metaphor for life.
I like #3's way of phrasing it! After making the choice and living with the consequences of choosing one path over the other, the speaker is reflecting upon that choice with the benefit of many years of hindsight. I don't think the speaker is sorry about the path chosen, but is simply recognizing that there were other experiences in life that s/he missed as a result of making the choice to follow the less-traveled route through life.
Aside from the fact that it is written by Robert Frost (who is notorious for his extended metaphors) I think it is interesting that the speaker concludes in the final stanza that the path he took was the "one less traveled by" when just two stanzas before that he suggests that both paths, though clearly different, have been worn "about the same."
It is as if he is suggesting the difference between the two roads was not apparent at the time of the decision, but in hindsight, he realized he took the one that most did not take. By very nature of the reflection and the suggestion that such wisdom can only come through age and experience, then the images in the entire poem come from an older/wiser perspective, further suggesting they are meant to be metaphors and not literal.
To me, the symbolism implicit in this poem is made clear in the final stanza, which asks us to think why it is that a common, everyday happening such as a rambler having to choose one path over another is something that will be remembered and retold years after the event. This clearly points towards this decision being symbolic and much more important than it first appears to be.