I'd go with the Wii.
The NES was home to some bad games, but many of the worse ones only appeared on the NES later in its life after it largely monopolized the market and Nintendo had secured a reputation for quality. The Game Boy accumulated a fair number of worse games, but that was largely due to its longevity as opposed to bad control, and it's worth noting that it even took Nintendo a while to make handheld games really worthwhile (many earlier games were inferior versions of NES games).
More recently, the DS had a lot of low-quality games, but considering the sheer size of its library (over 2000 licensed games), there were not THAT many terrible titles, especially when you consider that some of the worst DS games were licensed titles released on every platform under the sun.
Most recently, the Wii U has had some pretty awful things like Meme Run and the Letter, but on the retail side of things, trash without the word "Sonic" in the title stopped being released shortly after launch. Digital-only games include those terrible titles, but considering how Nintendo is currently making relatively large strides in the console digital market, these mistakes are more than outweighed. For example, the Wii U eShop got Shovel Knight, Guacamelee, Child of Light, Telsagrad, 1001 Spikes, SteamWorld Dig, and Stealth Inc 2 from outside developers in 2014 alone. Besides, it's not as if other platforms had no terrible games this year. The only reason we remember Sonic Boom instead of the Rambo game, Yaiba Ninja Gaiden Z, Escape Dead Island, and Soul Calibur: Lost Swords is that Sonic always attracts more hype. And if you want digital disasters, check out every other product released on Steam this past year.
The Wii is different. It was seemingly built on the assumption that few would make high quality games for it, which was a bad way to start. But even after it became popular, the initially low standards were never high enough to keep hundreds of shovelware titles from coming out, to the point where both buyers and even dedicated gamers and reviewers could not keep track of what might or might not be good. Unlike the DS though, few skilled developers outside of Nintendo ever made much for the system, which reinforced the notion that the Wii had no quality games aside from Nintendo's, leading to consumer apathy, and eventually bad sales for what good games did eventually come out.
I think that this is one reason why games like Little King's Story, No More Heroes 2, Red Steel 2, and some multiplatform games from about 2009 onwards had poor sales despite good reviews and the Wii's installbase and general popularity into 2011. Of course, the fact that many of the Wii's games were more niche than their HD counterparts (was MadWorld ever going to outsell God of War?) didn't help either.
Oh, and WiiWare didn't work out. It came out over a year later than preferable, had to compete with a healthy Virtual Console. At this point, the VC in North America already had over 200 games, which probably was a bit to compete with. The Wii's storage limitations were also a big problem. Even after SD Cards became an option, 40 MB is less than preferable to many developers. On the 360, Super Meat Boy, Limbo and Minecraft were in the 100 to 125 MB range, Castle Crashers was 140 MB, The Walking Dead is over 400 MB.
