Next Generation was the US import of the UK's EDGE Magazine, which is still around; Amazon sells subscriptions and B&N carries monthly issues at their stores for $8.
Next Generation's best days were '95-late '99 or so, before the "NextGen" domestic redesign and loss of content. They were among the most journalistic publications for any industry - for whatever that's worth, granted that their topics of choice weren't as important as international politics. One of the more memorable was an issue in 1997/early '98 that asked on the cover what was wrong with the Nintendo 64, subsequently argued with the expectedly lengthy, multi-part article, with plenty of comparison photos, and crowned with an interview. (Next Generation interviews were second-to-none.) That may sound at first like what 1up attempts every other week beside "Fifty More Worst Game Boxes Of All Time", but having the centerpiece of your gaming magazine question whether the most hyped console in years was even viable wasn't passé then, and to argue it in a dense, cohesive article longer than many review sections would still be a welcomed deviation from the norm.
I still have all of my Next Generation issues, including their premiere, and read through them once or twice a year. You could quibble, especially with review scores. (Issue 03 gave Mortal Kombat II on the SNES a relatively rare *****, and Snatcher on the Sega CD ***.) Quality was sometimes uneven as they tried different styles and emphases. But all told, it was a hell of a magazine and my favorite by far.
There was also a card bundled for three free issues of Next Generation with the first run of the US Playstation. I'm not sure why that was the case.