A while back I pulled out an old ep of Wipeout and while watching the credits, noticed that they gave promotional consideration for Kaepa(sp?) for the "footwear" used on the show.

Considering the fact that all game winners who played the end game wore tennis shoes, did the contestants get to keep the shoes?

It seems funny to say, "I didn't win the car, but I did get a lovely pair of cheap-ass, no-name running shoes to show for it" along with the $800 from the main game.

Were there other shows that gave away weird and unusual parting gifts or clothing to their players? (I don't consider home games as weird or unusual).

Yes, they got to keep the shoes. Peter even mentioned that a few times to the champions before the bonus round began.
All players on Illinois Instant Riches were permitted to retain the T-shirts they wore in the Knockout round as well.
I know IIR wasn't a national show, but it was on a superstation.

That "tic tac toe" jewelry seen during the end credits of 70s Squares shows is unusual. A one year subscription to US Magazine on Catch Phrase is also. Home games that weren't the games of the actual show could be considered "weird or unusual", i.e. the TPIR, Jeopardy, Newlywed, Wheel, and/or Dr. Ruth's Game of Good Sex games given to losing contestants on Davidson HS during the first season.

How about a box of Tootsie Pops that losing contestant's got on later years of Feud?

Tootsie Rollls/Tootsie Pops got a lot of end-of-show fee plugs on game shows other than Feud at the time, so that's not as oddball as one might think.

Later eps also offered a Peter Marshall collector's plate (the NBC finale among them), and jewelry-wise, early eps of $otC also saw losing contestants recieve a pendant w/the show's logo, one of which was sold on eBay by some former contestant a year or 2 ago.

Chuck Donegan (The Illustrious "Chuckie Baby")

Wipeout wasn't the first to giveaway shoes, either.
Kids on Double Dare (Reeboks), Finders Keepers (Converse), and Fun House (British Knights), all got a pair of shoes as well.

...and let's not forget the Whammy! Croton watch.