What are the cheapest/shorter flights from Amsterdam, The Netherlands to Lima, Peru and viceversa ?
The flights I've found stop over at Madrid, and are around 400 euros (Amsterdam to Lima) and 700 (Lima to Amsterdam) in March/April.
Shortest flight is direct one, operated by KLM. It's 12 hours. And it isn't cheap, standard price currently stands around 1300€ for return ticket (AMS->LIM->AMS), and if you're very specific on dates it might be even more.
Alternatives with one stop over: Delta (via Atlanta), Air Europa (via Madrid). It's might be slightly cheaper (1000€-1200€), but instead of 12 hours, that would be more like 20-30 hours.
The Air Europa route (AMS-Madrid-LIM) had a reasonable stopover in Madrid and was somewhat cheaper than the direct KLM flight. However, if you book sufficiently early, the difference may not be that much between the KLM and Air Europa flight.
A reason to go for the more expensive KLM flight may be that the Air Europa flights seem to have a higher risk of being cancelled. My return trip in March 2012 was combined with two other Air Europa return flights (12h earlier and 24h earlier), impacting my holiday planning somewhat. If you have a scheduled trip in Peru, this might be impractical. With KLM you may have a smaller risk of this occurring. Given the price difference (when booking sufficiently early), I may personally opt for the direct flight next time.