The Prevalent Wii Pun is not a Pun
Since when did anyone say "I'm going to play with my GameCube?" You think you've heard that a hundred times, but before the Wii, you hadn't. If we said it like that, it makes it sound like GameCube and me are going to run around the backyard, kick a soccer ball, jump on the trampoline and cool down with some Otter Pops.
I'm going to play with my Xbox.
Is not something you'd say! I don't know about you guys, but I'm going to play a video game on my Xbox or "I'm going to play Xbox."
Seriously who (other than modders) is going to say "Let's play with my Xbox today..." We never hear that! We hear "let's play Xbox now."
Maybe things are different in your region, but if this is the case, then someone saying "I'm going to play with my Wii" is not an innovative joke but rather far-fetched. The only reason anyone would say that, other than when they think they've discovered some amazingly creative pun and want to get a laugh, would be from the fact that they've had it pounded into their memory by the millions of folks who ingeniously came about such an "original" pun... that isn't even a pun!
In the defense of the people who say this joke, we haven't been given many options, our other two choices to express this thought across are I'm going to play on the Wii... or... I'm going to play Whee! But before you decide to bash the Wii's name, or decide to repeat back to your friends a "joke they've never heard before", just stop, and ponder about how we aren't in the predicament that the French are, who might find themselves saying I'm going to play the yes!