RTA is giving away free Day and 30-Day passes in a drawing- simply send in a 1-day or 30-day pass that was valid on June 17th, and you'll be entered into a drawing for 100 free bus passes. The agency has more information here.
If you're in Omni territory, you can get a free ride all day on Thursday by visiting Omni's web site and downloading this flyer, which can be exchanged on any Omnitrans bus for a free day pass. Please note that Omni is only accepting flyers printed in colour, so don't print it off on the office laser.
Me? I'll be entirely disregarding Dump the Pump day, hurtling down I-80 in a fossil-fuelled vehicle, but know that I support the campaign in spirit!