There is already a lot of info here, all I can add is my own personal findings when I looked into this.
One of my previous Audi A4's was a 143bhp, I looked at a remap (Revo remaps, meant to be one of the leaders in this area?) over a plug in box for a couple of reasons.... I was advised the remap re-writes the brain basically, tells the engine what fuel, air and so on to mix to get the best output, as a result you get better performance and better mpg. I have a couple of friends that have gone down this route and love it! In addition, as already mentioned in this post, if for any reason it gets wiped the supplier will upload it again for you (usually free as an existing customer). I was told that the software was undetectable so in the event of an accident no-one would know it was there, which also means its up to you whether to declare it or not. I then approached Audi and asked the question, they advised its not that simple and if you start running 177bhp on a 143bhp car then it will break - reason being the radiator nor the turbo is built or big enough to do the job over a long period of time. I must admit their response made sense, but I cannot comment on how true?
The other option, a plug in box. My mate has an A4 177bhp, this now runs just over 200bhp, he loves it and it does the same job. Difference is, IF he ever had an accident he would need to rip the box out or insurance invalid (if not declared), if after an accident you dont have time to do this
then clearly no claim!
I never had it done in the end, I'm tempted even now, but to be honest I don't think I ever will.