The practice of odds-giving never entirely vanished and it's still practiced today at various clubs, especially in their handicap tournaments. Most handicap tournaments do not use material odds, but of the ones that specify that particular type of play, the Hobart International Chess Club of Tasmania serves as a fine example. This club was formed in 1994 by acquiring the equipment from the original Hobart Chess Club founded in 1887. They hosted blitz odds tournaments. Their method of applying odds is that the stronger player must offer 1 pawn's worth of material for each 100 pt. rating difference. Another such club is the Winchester Epiphany Chess Club of Winchester, Massachusetts. Their "Herbert Handicap Chess tournament," played at 20/10 has a very specific formula, listed on the link above, for who gets what odds.
The idea of "1 pawn's worth of material for each 100 pt. rating difference" seems a bit extreme to me, since I can hardly imagine getting two-pawn odds from even one of our strongest masters. A more reasonable rate might be a pawn per 300 points, since I have given piece odds with success to 1100 players and can almost imagine someone of Kasparov's (or Rybka's!) strength being able to spot me a piece. Likely a time-odds tournament would be even more attractive to higher-rated players.
What do people think of an odds tournament some day at the Kenilworth Chess Club?