Origin unknown. Lately popularized by the country band Big & Rich’s 2004 “Save a Horse (Ride a Cowboy)”. This is a popular one for bumper stickers and license plate frames. X is things a person can be said to ride, and Y is the canonical rider of X, so variations on this snowclone tend to sporting themes and sexual innuendo.
Other variations spotted in the wild: Save a wave, ride a surfer; save a sidewalk ride a skater; and my favorite from Harry Potter fandom: Save a broom, ride a Quidditch player.
The sporting theme can also be seen in [the as yet unposted-about] “Give blood, play X” snowclone.
[Edited to add: “Save an X, Y a Z” is also a possible variation, as Lance Fisher reminded me. The example he gives is “save a tree, eat a beaver,” and I’ve also seen “save a cow, eat a vegan.” I don’t think possible Ys are restricted only to {ride, eat}, though again there is a louche connotation in one of these examples, which seems to suggest that Y is limited to words that can stand in for sex.]
The Snowclones Database 
Love all this snowcloning. See my writeup at http://www.figarospeech.com.
I’ve also seen Save a X, Y a Z. As in “Save a tree, eat a beaver.”
Surely it’s “Save a tree, eat a beaver,” rather than the reverse?
blast from the past:
“Save an alligator, eat a preppie.”
Like the site 🙂 I saw a variation of this in the 1998 movie Desert Blue. There the characters talk about a bumber sticker that reads: “Save a donut, shoot a cop”
I’ve also seen a variation that is simply Save X, Y Z. (where X and Z are tangentially related nouns, and Y is a verb related to the use of those nouns). For example, I saw a shirt that said: Save water, drink beer.
I’m speculating here, but given that most of these examples imply a conservationist bent, I wonder if they don’t derive in some way from Woodsy the Owl’s “give a hoot, don’t pollute.”
In an old episode of Roseanne, she has a confrontation with a trucker who has a bumper sticker that reads, “save a whale, harpoon a fat chick”.
This one is kinda common among some dragonkin:
“Save a virgin, ride a dragon”
“Save a whistle, blow a lifeguard”