I have a few arcade titles for the Xbox 360 (Walking Dead 1 & 2 and Wolf Among Us) and am wondering about the compatibility of these titles on the Xbox One. Will I still have access to them, or will I have to pay for them all over again to play them on my Xbox One?
This entirely depends on the game.
For most Xbox Live purchases, the answer is no. Since the Xbox 360 and Xbox One have a completely different architecture, binaries are not compatible between them. For a game to be released on the Xbox 360 to be released on the Xbox One, it must be specifically released for the Xbox One. Due to this, many games available on the Xbox 360 Marketplace simply are not available for the Xbox One.
Some games offer a free upgrade. For example, Call of Duty: Advanced Warfare allows people who purchased the Xbox 360 version of the game to upgrade to the Xbox One version for free. The same goes for PS3 players, they will get the PS4 upgrade free of charge.
Other games offer an upgrade for a reduced price. An example would be Minecraft:
Owners of Minecraft: Xbox 360 Edition can upgrade to Minecraft: Xbox One Edition with a substantial discount. All downloadable content previously purchased for the Xbox 360 Edition is available free for redownload on Xbox One.
Finally, some games you simply must purchase again. Plenty of games have been developed towards both platforms, and have released for both the Xbox 360 and Xbox One. These games you would have to purchase again if you wanted to "upgrade" to the Xbox One.
The games you mentioned (Walking Dead 1 & 2 and Wolf Among Us) fall under this category. While the games have been re-released for the Xbox One, it is a full purchase. There is currently no free or discounted upgrade program for these games.