The World Tree motif, with Yggdrasil as the main model, has made its way into several video games, one of them being Faxanadu.
Yeah, THAT game, which involves the hero climbing the World Tree from its roots to its branches, and also involves Elves and Dwarves from Norse mythology. We rented the game once when I was a kid, but we didn't get very far. We DID watch the Captain N episode based on the game, however, in which the King of the Elves was an Elvis impersonator.
Another video game series that involves the World Tree is Dragon Quest. As early as the second game, there's an item awkwardly called "Leaf of World Tree," which can be used to revive a fallen hero. In more recent games, the item is called an "Yggdrasil Leaf," making the connection to Norse mythology more obvious. This is part of the same renaming that has Wyvern Wings now referred to as Chimera Wings, which I don't really care for. Apparently they've always been Chimera Wings in Japan, but even though a Google Image Search found some pictures of mythological chimeras with wings, isn't "Wyvern" a better name for this sort of monster?
Getting back to the World Tree, though, you can find the Leaf in DQ2 on a tiny island that I believe is said to house every kind of tree in the world (although the eight-bit graphics don't really present this too well). I believe the only Leaf to be found in the upper world of DQ3 (which is an analog of our own) is in a large forest in the area corresponding to Siberia, and the Siberians DID have a World Tree myth, so maybe this isn't entirely coincidental. But the first DQ game that actually has a World Tree is the fourth. The base of the tree is in Elfville, and its leaves are free for the taking, but I believe you can only have one at a time. The Zenithian Sword is also hidden somewhere in the tree's branches. The World Tree is also significant in the Dragon Quest Monsters games, which include kingdoms like Great Log and Great Tree.
And while I'm on the subject, I feel I should also mention the Deku Tree and Maku Tree from the Zelda games, which aren't exactly World Trees, but have some similar characteristics.