There was some big controversy about this a few months back. Some guy's wii u broke and nintendo said the games were tied to that one system only (i.e., they don't transfer to other systems). So when you digitally download you can only use it on that one system only. If your shyt breaks, you gotta buy the game again for your new system.
That sound like some bullshyt. I'd be fukking pissed.
Nah, your ok. When I first bought my wii I registered it online for the warranty and all of that, then it bricked. I sent it to nintendo and when they sent me a new one, I had to call and give them the nintendo id on the bottom of it and they had my original one from when i registered it. He did something on his end probably took like 2 mins and he said "go to the e-shop and pick up a game youve bought" I selected metroid and it said purchased, I just had to redownload.
I did the same with my wii-u when I bought it. I had a problem with mk8 and the free windwaker. I called nintendo, he pulled the nintendo id from the bottom of my wii and basically saw all the titles ive bought in eshop, and said "no problem, give me a minute" told me to check windwaker and it said "download"
The only thing you have to do is make sure you do the warranty shyt, and its different from club nintendo I believe because even though I had my warranty and was registered as the original owner, my club nintendo was not in sync'd with my wii-u which you do from the eshop menu.
Therefore you can add a bunch of money (like right now I have $40) sittin in my eshop account. If someone breaks in and steals my wii-u. I can call nintendo, they can pull up my stuff by my name and address + telephone number and disable my wii-u nintendo id, therefore they cant spend my money, plus you can save your credit card info to your wii-u. So once you get a new wii-u you it is possible to obtain your titles and such back.