It also depends on the type of design you’re doing as well. The format of the design should just be another tool at your disposal - the canvas of your painting. The size (standard, non-standard, large or small) should be considered based on your design and message more than on what is standardized. Presenting a design in portrait or landscape will affect the message.
The only real plus for sticking to standard sizes is saving money when it comes to printing - which is why I think it usually IS a good idea to include a 4x6 (seems to be the most common and cheapest for buyers to print and distribute) - but don’t get stuck in the 4x6 rut. Also keep in mind other factors that may limit your audience and possibly turn buyers away from your item.
Something else to consider is using unique sizes and/or special printing techniques. I’ve seen a few designs that deviate considerably from the standard print sizes, but the flyer category could use a some mixing up as far as sizes.
I rarely see flyers setup for die cutting, embossing or separations. Flyers don’t have to be square, and I’d love to see some crazy high-end flyers with incredible die cut options - for those buyers that want to invest in a decent print job.
Let your design dictate the format, but always try to include something practical.