Amp sims have come a long way over the last few years, to the point I wouldn't be too unhappy using one for "modern" heavily compressed and distorted sounds. Unfortunately, I don't use that kind of sound that much :-(
I put a real effort into them for most of last year, especially Amplitube which struck me as the one offering closest to what I'm "used to". In particular because it let me model the key components of one of my live rigs, a Fender '63 reverb tank feeding a Tiny Terror into a closed back Celestion. There's a few other things in the rig as well which Amplitube doesn't model but provides alternatives. In the end I came to the conclusion the sim just doesn't cut it. Sure, it has some of the characteristics of the hardware but it's still just a pastiche.
The sims simply do not respond like valves, springs, cones and transformers do. At least, not so I can feel "right" using them. Getting the sim to react correctly to a Tele as compared to an SG is a lot of effort that in the end I don't find worthwhile.
A pity really because being able to track "raw" guitar without having to commit to tone, fx etc. at the tracking stage is undoubtably useful.
So I've gone back to the amps and a chain of pedals. Including a Blackheart B1H1 "Killer Ant" which sounds seriously nice, produces about 1/4Watt and goes into the beginnings of breakup at levels that are very domestic.
The other side of the coin is that I've heard people use PODs and VSTs very effectively. So I accept it can be done, just not by me without my synesthisia protesting.
In the analogue realm I also use Sansamp character series pedals sometimes as part of a full-range rig. The Blonde in particular does a pretty good sound-and-feel-of-Fender - better (in my opinion) than most of the VSTs I've tried. In the end I suspect it comes down to a matter of touch and feel and is very much an individual thing.
I have the same reservations with synths, the emulations somehow lack the punch and cut of much of the hardware, especially analogue. VSTis can sound OK to very good in a mix, but add in something like a real MS-20 and preventing the real from stamping all over the virtual can be quite tricky. Mind you, I'd rather deal with the VCS3 app on my iPad than the unpredictable weirdness of the real thing even if the app doesn't sound quite as wild or good.
Oddly, having said all that I'll happily use emulations for the mixing/mastering stage and as plugin processors/effects on hardware synths. Yes, I know that's a contradiction but....