The three most anthologized Frost poems are probably "Birches," "The Road Not Taken," and "Stopping by the Woods on a Snowy Evening." I like these, but my top three would be "Design," " One Acquainted with the Night," and "After Apple-Picking."
Frost is a 20th Century modern American poet. Though he often writes about modern themes such as loneliness, alienation, desolation, he, unlike most modern poets, usually uses a strict structure. Most of his poems rhyme. I think his structure and rhyme make him easy to remember and quote.
Also, much of his appeal lies in his deceptively simple lines. Frost uses a simple vocabulary to convey his ideas, and yet the ideas are quite complex. A poem about ground being covered by snow becomes more a statement about man's own desolation, as in "Desert Places." A poem about trees in an ice-storm becomes a statement of the desire to temporarily escape the world's troubles and woes, as in "Birches." A poem about two paths in the woods becomes a poem about individual choices, as in "The Road Not Taken." Most readers enjoy the depth of Frost's poems as well as their simple elegance and well-crafted structure.
Some of Frost's poems are also known for their complex narratives conveying important, realistic themes.
For instance, "Out, Out-" is one of Frost's most famous poems. It depicts the death of a young boy, and all the circumstances surrounding the death while making a commentary on the briefness of life, and what little impact death actually has on others.
"Home Burial" is another narrative poem that deals with an intense issue in the human condition. "Home Burial" depicts dialogue between a husband and wife who must bury their child. The dialogue and emotion is so realistic and emotional that the poem can even be played out as a dramatic scene.
I think, really, Frost's diversity within his own canon of work is what makes him so popular and widely studied today. There is really something for everyone within a Frost anthology.