ANR is necessary if you fly around 25+ hrs a month, or if you fly a R985, Garrett, or other loud plane.
If you are flying something like 10hrs a month in a 172/PA28/cirrus/etc a nice set of David Clarks with the gels will do just fine.
IMO all the guys that put some hours on their headsets tend to lean towards:
Lightspeed (ANR), I've been running the Zulus at work for 3 years not, I like em, minus they are made in china which kinda sucks.
Bose (ANR), lots of guys like them, they seem fine when I've worn them
David Clark (passive), industry standard headset, MANY guys from backcountry pilots to acro guys swear by them.
My pax set is a DC 10-56 with the oregon aero goodies
(
http://www.oregonaero.com/headset-upgrades/headset-upgrade-kits),
ALMOST as quiet as my Zulus. Basically DCs are like the Zippo lighter of headsets, they will last forever, made in the US and have great customer support.