My parents have taken advantage of Southwest's senior fares, which are almost as cheap as their Promotional Fare Specials:

Southwest Airlines Fares (QCD)

Senior Citizens Fare:
One-way fare
At least 65 years of age
Passengers must present valid I.D. showing proof of age.
This fare is not available for purchase through Ticketless Travel Online.
Senior fares are not eligible for Rapid RewardsSM Double Credit.

It doesn't mention it's nonrefundable, which would be nice in case illness would postpone taking a trip...