Most of the seeds commonly used to feed birds will germinate when the conditions are favorable. Sunflower seed sprouts in particular look "odd" and make the lawn feel different when continuously mowed.

You can reduce the problem by cleaning up spilled feed (a wet/dry vacuum works) or placing feeders where the seeds will not fall onto the lawn. You can also avoid spillage by choosing feeders designed to catch fallen seed and selecting feed preferred by the species you want to attract. Removing feeders in summer is another option.

Birds are messy feeders. An alternative method to deal with strange plants that come up under bird feeders is to create a circular area (3-4 feet in diameter) free of turf. Place a border around the perimeter, fill the area with very course sand or wood chips, shaving or sawdust. This will attract ground feeding birds to clean up after their messy cousins. This will also increase the types of visitors to your yard, and make it easier to remove sprouts that get missed by both groups.

Here are links to more information:
http://extension.oregonstate.edu/news/story.php?S_No=90&storyType=garden
http://www.ca.uky.edu/agc/news/1999/Jul/birdbuzz.htm