Whether you call it Yankee Swap, or White Elephant...it doesn't matter...there always seems to be a discrepancy in the rules of how to play.  Whether it's #1 gets to pick any gift once all gifts are open or you have to exchange your gift before unwrapping it.  Let's see if I can clear up the rules a bit...

According to SecretSanta.com...their rules are similar to how I'm used to playing:

In Yankee Swap each participant brings a wrapped, unmarked gift and places it in a designated area. Guests are given numbers as they arrive, or their names are randomly drawn, and they select and unwrap gifts from the pile in that order — with a twist.

The person who receives the number 1 will pick a gift (that is not their own) from the pile and open it for all to see (or models it, reads it, or demos it). During the selection of a wrapped gift, the participant may visually inspect the gifts, pick them up and/or gently shake them.

The person who receives number 2 then chooses a gift and opens it, and then must decide whether to keep it or swap it for the first player’s gift. Each person in order then gets to select a present, open it and decide whether to keep it or swap it for any other gift someone has already opened.

Opening of gifts and swapping takes place until all the presents have been chosen. Finally, the person who picked first gets to choose from all the gifts or keep what he/she has already received. In the end, the gift you are holding is the gift you take home.

So?  Is this the only way to play?  Here's a fun little alternative to add to the above set of rules (I want to do this next year!)  According to YankeeSwap.com:

Here’s another twist on the traditional Yankee Swap, after the last person’s turn, the first person has the option of keeping their current gift (in which case the game ends), or they can exchange with anyone else. If they choose to exchange, the person they stole from now has the option of either keeping the gift they were given, or exchanging. This game only ends when someone decides to keep their gift. 

According TalkingCents.com, they twist up the rules a bit.  (not exactly sure how I feel about this option)

  1. Gather up a group of friends and/or family and find out if they want to do a Yankee Swap.
  2. Determine the price limit/range for each person to spend.  This ensures that everyone spends and receives the same value.
  3. Each person will buy 1 gift, wrap it, and bring it to the party (do not tell anyone what the gift is, or label it in any way).
  4. Once you are all gathered, place all the gifts in one area where everyone can see them (in a pile, under a tree, whatever).
  5. Put numbers in a hat for the number of people that are participating (ex: 10 people = Numbers 1-10).
  6. Everyone takes turns drawing a number until everybody has one.  This determines the order of gift selection.
  7. #1 picks a wrapped gift from the pile and opens it.
  8. #2 has the option to A) take the opened gift from #1  or B) Pick a gift from the pile for themselves.
  9. If #2 takes the gift from #1, then #1 picks again.
  10. #3 has the option to A) take either of the previously opened gifts or B) Pick a new gift from the pile.
  11. Whoever gets a gift taken from them must pick a new one, but does not have the option to swap.
  12. This carries on down the line.  Everyone has the option to take any gift that has already been opened, or take a chance on a new gift.
  13. Here’s the kicker… Once all the gifts are opened, #1 has the option to swap with anyone else.  Essentially getting to choose any gift he/she wants.

All in all, it really doesn't matter what version you play...just as long as you remember:

DO:  Have fun!!

DON'T: Take the game too seriously and get upset.