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It's always possible that you might get a bad unit, but most of what I've heard indicates that they are all pretty good. Your best bet though is to read reviews of the console you want to buy, particularly reviews by customers who already own them. That way you'll know if there are any issues or problems you might encounter before you actually buy the unit.
See Amazon's video games page to start finding customer reviews of all the latest videogame consoles.
As far as I know, no console of the current generation (Wii U, PS4 and XBox One) have suffered the same sort of reliability issues that were experienced with some of the previous generation consoles. There were some early reports of Wii Us having an issue when you ejected a disc while the console was powered down that required the user to unplug it for a reset, but I don’t think it was ever widespread and it seems to have been resolved. Some PS4s had an odd issue that caused the unit to power up after it had been shut down and eject the disc that had been left in, but this doesn’t seem to be all that common either. There were some issues with PS4s having issues out of the box and having a BLOD (Blue Light of Death), but the numbers were apparently very low, in the 0.X% range. The XBox One doesn’t seem to suffer from any widespread issues either.
Of course, you could always get a lemon, but that’s true with anything. I saw an article recently that suggested this may be the most reliable generation of consoles ever (not sure if he remembers the old days of reliable Atari 2600 and NES consoles), so improved quality control and design may have trumped the early release problems we have seen in the past decade or so.