Let me turn my hearing aid up a bit........wait, it's all the way up and I don't hear anything. Mine was built in November of '05. The 2.2 purrs like a kitten.....almost. It's going to make a little noise, after all, it's a little motor.

 

I am somewhat noise sensitive in that I have a hard time hearing conversation with even moderate ambient noise (I worked in a machine shop for a few too many years with no hearing protection) and I don't have a problem with the engine noise. My problem is with the wind noise when I have the windows down. I have the 2.4L engine with stock exhaust.
By the way,

 

While our salesman was tracking down an HHR that matched what we were looking for, he gave us a 2007 LT to take for a test drive (we bought an 06 LT).

The 2007 was quieter under acceleration than our 06 is, but I don't find the noise level that bad.

It's certainly quieter than other GM cars we've had (i.e. 2001 & 2003 Malibu).