I'm a big fan of racing games, and it seems like there are not a lot of them around these days, so I'm happy that NfS exists, even if the quality of the games has been very variable over the years. Shift is not representative of the games as a whole, it being far closer to Forza/Gran Tourismo simulation (but not quite) whereas most of the others have been closer to Burnout Paradise.
If you own a PS2 then Underground and Underground 2 were some of the best arcade racers around in that generation. This (just gone) generation the series has been very rocky. Basically
2005 Most Wanted
2006 Carbon - both games were solid enough but really showing their age now. Both city racers involving illegal street racing and police chases. Carbon was basically Most Wanted but at night and was also way to easy.
2007 ProStreet - total failure, tried to get rid of the open cities in favour of track based racing; like Forza but replaced the handling with obnoxious attitude.
2008 Undercover - another total failure, back to street racing, but badly implemented, ugly and with really weird handling. Also cringe worthy FMV acting.
2009 Shift - you know about; very credible first go at a simulation style racer
2010 Hot Pursuit - after Undercover, EA brought Critereon (aka the Burnout guys) over to the franchise. The result was a much better racing game that focused on multiplayer. Was a little bare-bones as a single player experience.
2011 The Run - another failure; supposedly a story-based coast-to-coast race across America, but suffered from some really annoying gameplay. It does look quite good and I actually ended up playing it a lot, especially the multiplayer. Not sure I'd spend much effort in defending it though.
In this year EA also released Shift 2 but downplayed (or removed entirely I'm not sure) the NfS banner from it.
2012 Most Wanted (again) Critereon's second NfS game combined element from Burnout Paradise and the NfS series. Its one of the better NfS games, but since most of the stuff that works was cribbed from Burnout and much of the stuff that doesn't (i.e. police chases) from NfS, that's hardly high praise.
2013 Rivals - haven't played this yet.
2014 series taking a breather.
So to basically answer your question, the series as a whole gets negative press because we've had nearly a decade of some very mixed games, many of which have little to do with one another. At this point the words "Need for Speed" mean nothing more than "racing game published by EA".
Despite the fact I've been quite negative here, I've played nearly all the games and enjoyed most of them in a limited way. I'd classify them in the following way.
Genuinely good - Most Wanted (2005), Hot Pursuit, Shift, Most Wanted (2012)
Iffy but fun - Carbon, Shift 2, the Run
Not fun - Pro Street, Undercover
Typing it out like that, it's not as bad a record as I initially thought.