Let's see now
NES sold 34,000,000 as of January 2010
SNES sold 23,350,000 as of January 2010
Nintendo 64 sold 20,630,000 as of January 2010
GameCube sold 12,940,000 as of January 2010
Wii sold 35,910,000 as of September 2010
Game Boy sold 44,060,000 as of January 2010
Game Boy Advance sold 17,640,000 units as of January 2010
Game Boy Advance SP sold 24,000,000 units (both combined = 41,640,000) as of January 2010
Nintendo DS/Lite sold 39,960,000 units as of September 2010
Nintendo DSi sold 7,720,000 units as of September 2010
Nintendo DSi XL sold 1,600,000 units as of September 2010
So far, the Game Boy and Game Boy Color, combined is the biggest selling console by Nintendo, in the US, however, when you combine the sales of the Game Boy, Color, Advance and SP, it comes to 41,640,000 as of January 2010), however the DS, DS Lite, DSi and DSi XL sales come to 49,280,000 as of September 2010 (by now, it's more than likely over 50 million).
While the DS (and Lite) are individually not the best-selling, the DS series as a whole is the best selling console series.
Now, what about Microsoft and Sony?
PlayStation has sold um... stuff this. Let's just say the PS1 has sold over 100 million worldwide, the PS2 is almost 150 million worldwide and whatever... I can't be bothered to search for how many of each console was sold IN THE US (And not worldwide).
I can say that the DS series combined totals some thing like 135 million, which makes it the biggest selling handheld series (if you count the entire Game Boy as a series from Game Boy to Game Boy Micro, and all the PSPs from PSP-1000 to PSP Go, as a series).
Globally, the PS2 is the best-selling console of all time, but as for the US, I have no idea.
Remember this, the DS hasn't sold 47 units in the US... (just), because as of September 2010 it was 49,280,000. I'm pretty sure that in 3 months, another 720,000 could have been sold, maybe? I.e. not 47 million DSs sold, but more like OVER 50 MILLION.