There's nothing inherently wrong with normalizing files, just don't normalize to -0.1 dB. It doesn't leave you any room for further manipulation, such as an EQ boost. Even normalizing to -3 dB puts you in pretty much the same boat. -12 dB is probably a more practical ceiling. AT's suggestion of -18 dB is a good target.
 
One of the issues, as you discovered, is that the normalization process looks at raw sample values, not "true" peak values, which are often higher. That's why when you normalized to -2 dB you subsequently saw 1 dB peaks. That can be avoided by keeping sample peaks below -3 dB, but that still leaves too little headroom for mixing.
 
All of this is really moot, though, since there are only a few situations where normalization is warranted. If, for example, if you had multiple takes of the same instrument at wildly different volume levels, normalization could quickly get them into the same ballpark. Even then, you'd probably only bring them up to peaks between -18 and -12 dB.

Exactly, Like I said, you need to understand what it is, and what it does, and what it can destroy if abused. 
 
Another example where turning up a track is useful is when trying to use Audio snap for drum replacement. It's nice to have the peaks maxed out so audio snap can read them correctly.
As always when applying destructive editing, keep a back up of the original.
With drum replacement you can even have overs as the audio track will not be used in the end, the Midi track will be all that is needed. 
 
And Bit, your scenario is where it's nice to actually have a RMS average of the takes. Another feature that requires a tool copy to a wave editor. Craig Anderton is interested in looking into adding a few of these type of features :}  

We digitize thousands of tapes and vinyls yearly with Sonar. We have already normalized 100.000 times.
This all works perfectly with Sonar since over ten years.
But it must in no case any plugin in the effect-bin.  And the gain and volume must be set to "0".
Otherwise plugins and gain and volume change the level.
When normalized to -2db all other audio-software will show -2dB. That works absolutely perfect without any fail.
 
 

I'd read an interested article about normalizing audio files, in which they discuss "inter sample peaks" that can be introduced in the outputs. If you normalize too close to zero, you can end up clipping your output section. Someone more tech-savvy than I can explain it better. Here are a couple links relating to MP3 conversions, though a proper google search should help locate a more meaningful discussion as it pertains to working in a DAW.
 
http://www.producenewmedia.com/?p=497
http://www.hydrogenaudio.org/forums/index.php?showtopic=85571
 
Whether or not normalizing is actually "bad" is a topic that will probably be debated for generations to come. I've stopped doing it, except in instances where I might be working with a poorly recorded track and my volume/gain adjustments just aren't cutting it. In those rare situations, I've gone no farther than -1.5 max. 
 
 
 
 
 

What I found somewhat startling to realize is that making a cut with an EQ can also result in clipping/increased peaks. In effect, if you cut a frequency but that frequency was actually inhibiting another peak, you're creating a higher peak. It's not usually a big issue but if you're skirting so close to 0dbfs it can come into play.

In real-world digital audio recordings, inter-sample peaks seldom exceed 1-2dB, and any decent DAC has enough headroom on the analog side to accommodate that.
 
As far as I know, the vast majority of audio processors, like SONAR, do not perform a virtual DAC operation or oversampling when normalizing. They just set the highest sample to 0dBFS (or whatever you specify as the normalization reference) and raise everything else proportionally.
 
In a typical audio clip of any musically useful length containing a real-world signal, there's usually a peak sample value somewhere in the file that is extremely close to any inter-sample peak that might occur elsewhere in the track; combine this with the headroom built into most DACs, and it's just not an issue in the vast majority of cases.
 
Most of the examples of inter-sample peaking I've seen on the Web are either very short, non-musical, artificially-generated test signals and/or do not produce any audible distortion when played back through a decent converter.