I wouldn't cut it down. However, it is best to cut all flowering stems to prevent it from flowering itself to death (and ideally you would have done so about a month ago). The idea is to help it build some basal buds and foliage, hence improving the plant's vigor. Gaillardia flowers so rampantly that its energy is often put into flowering at the expensive of plant vigor. (See Tracy DiSabato-Aust's book The Well-Tended Perennial Garden for more information on overwintering perennials.) Good luck!

Gaillardias tend to be short-lived perennials in any case.

Maybe there's something to the idea of restricting flowering to promote longevity - but then you're defeating the purpose of having a long and abundantly flowering perennial.

My strategy is to keep new plants coming from seed, while deadheading sufficiently to keep the plants' efforts focused on growth and bloom, not seed production. Easier said than done if you have multiple garden chores (I just harvested a bunch of seeds from G. "Arizona Sun", which is in its second year. If it makes it to 2013, fine...if not, I'll have new plants coming along which will flower in their first year).

For existing plants, I'd recommend not cutting them back until spring.

^The main reason they are short-lived is wet winter soil and a lack of vigor brought on by excessive flowering. I don't feel that cutting them back a month or so before frost really deprives you of too much enjoyment when they usually start blooming in May and keep going all summer. But, they readily reseed, so it is no big loss if you happen to lose the parent plant.

Deadheading prevents reseeding but doesn't really divert the plant's energy elsewhere; by the time a flower blooms, all of the plant's dedicated energy for that bloom/seed has been spent -- hence the recommendation to cut budding/flowering stems a month before frost and not just deadhead.

Just to follow up: With some plants deadheading is also good at forcing a plant to produce more blooms because if it fails to go to seed, the plant will continue to attempt to flower in order to do so. Gaillardia blooms so incessantly that deadheading doesn't produce significantly more blooms -- though you might have a cleaner-looking plant and perhaps a slight increase in coverage.

Thank you all for the great information! I really appreciate it! I love my gaillardia's and don't want to lose them this winter. Northern Ohio winters can be brutal. I'm just going to leave them alone until spring.

Another thing to note is that Gaillardia cultivars do not always come true from seed. So if you have seeds, you have no guarantee you will get the same plant. Therefore, I do like to preserve the parent plant.