Usually, shape is a great help in identifying birds. Even here, when the bird is facing away, we can still tell that this is some kind of passerine. In this case, it's a rather chunky one with a tail of medium length and noticeably long wings. There's another clue in the photo, sunflower seeds—lots of sunflower seeds below the bird, which strongly suggests a seed eating bird.
The broad white edges on the greater coverts are distinctive. The pattern may call to mind Lark Bunting, but what little we can see of the face pattern isn't right for Lark Bunting. Our bird also has a dark crown (with buff tips to the crown feathers) that is bordered below by a hint of grayish coloration. Lark Buntings should show a stronger facial pattern with a border to the auriculars that we don't see here. Furthermore, the outer tail feathers would have relatively broad white tips, not uniformly pale edging as on our bird. Snow Bunting and McKay's Buntings are similar, but again, would show much more white in the tail, indeed be much whiter overall. Some of the longspurs may make good candidates, but again the face pattern isn't right.
Looking a bit more carefully, we see that the flanks of this bird show a tinge of pink coloration, as do the lowermost greater coverts. This combined with the distinctive pattern to the greater coverts only fits the Rosy-Finches.
Excluding juveniles (which look nothing like this bird), Gray-crowned Rosy-Finches show a much more pronounced and contrasting gray hind-crown. The gray is very distinct and there is a sharp border to the edges (except for the black on the forecrown, which often blends into the gray). Gray-crowned Rosy-Finches are also almost always darker and richer brown than this bird. Similarly, Black Rosy-Finches have a more distinct grayish crown than this bird and are much darker. While they may have frosty edges to the back, the nape on a Black Rosy-Finch would not appear as uniformly pale brown as this bird.
This is a fairly typical 1st winter Brown-capped Rosy-Finch, with an indistinct head pattern, frosty pattern to the upperparts and relatively white patches to the wings. I photographed this Brown-capped Rosy-Finch in late December 2004 in Custer County, Colorado.

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The following people (listed by submission date beginning with the earliest) submitted correct answers for the February Bird Photo Quiz—Brown-capped Rosy-Finch:
As stated in the quiz rules, answers must consist simply of the Common or English name exactly as it appears in the ABA Checklist.
The following list shows the number of submissions for each species guessed.
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The photo and answer for this quiz were supplied by Chris Wood.