Agree with Jeff and Chuck on this one. It's really subjective, but pretty much a necessity in my opinion with certain styles of music. For some things, a single instrument recorded right with that "up close and personal" sound is all you need. The intimacy it brings into the mix is what makes it literally have more impact for THAT particular situation.
The only thing about the video that I didn't like was the tracking part. Trust me when I tell you, on that second pass, if you smash your foot on the floor that hard, a mic like the Nuemann is going to pick that up to where you'll need to re-record the track. So I questioned if that really was in real time. I also have not had luck in all my years shooting a mic at a sound-hole. That said, those are my only issues with the video really. The technique and it's use is spot on. Oh yeah, he also made a mention of messing with timing. The whole thing about creating a doubled part IS about the timing not being quite spot on. This is what gives you "Stereo". If it's too perfectly lined up, it will give you a mono type sound and you actually lose some stereo spread.
I personally like to double track electric guitars and acoustic guitars. But I also like the sound of an X/Y mic rig on an acoustic too. Electrics in rock seem to just have a little extra something when you double track them. As for when to do this...it depends on the style of music as well as what YOU feel you need. I'd never double track drums, piano or bass. To me there is just no reason to do so yet there are no rules that state "you shouldn't."
Certain instruments react to this technique differently and you also have to keep in mind that some aren't really focal points. If you double tracked a bass, it would have to be for a bass oriented album. Bass to me is a filler instrument and doesn't need to shine from a doubled part. However, when we record bass, it is a good rule of thumb to record the sound the bassist likes as well as taking a DI out so you have some other things to work with. You may want to re-amp him or do something to the DI to blend it in. I do the same with electric guitars. Mic up the amps and use a DI as well so if I need to, I can re-amp the sound or run it through a plugin. It's just a safety net really but it can also give you more cool options to work with.
Drums, you definitely don't want to double track because they are all about timing. Again though, no rules that say you shouldn't. But to me, they make enough noise as is and if you allow for the human timing errors that create stereo to be apparent due to a double tracked drum part, it's just not going to sound good. In my opinion, I like to stay away from any solo instruments as far as doubling goes. I don't do it on voice because it gives me that "Ozzy" sound. There are times when I will double a voice that is singing the same part for impact on something, but I don't use it as a part of my common practice like a lot of other engineers do. If I can't make a single lead vocal sound good on its own, I keep recording it until it does. Doubling it in my opinion, only doubles the lack of performance x2.
So yeah, it's really subjective and something you'll need to decide per song or per style really. It will, in my opinion, always make a sound bigger than say a HAAS effect where you clone a played track and move the clip a few increments or use a delay with a HAAS setting. That has its place too...but I prefer two independently played tracks when I need them. :)
-Danny