Basically, no. As my Colombian flatmate in London put it, every time a revolution occurs, the first thing that gets hit is the infrastructure, and down goes the rail. Not sure how accurate that is in all countries, but it's certainly the case in Argentina, Chile, Bolivia, Peru, Ecuador, and Colombia.
There are some limited train options in Argentina - from Buenos Aires to nearby cities (like Rosario). However the buses are cheaper, and faster, and it's not far, so why you'd take the train I'm not sure.
There's also a train from Ollantaytambo to Aguas Calientes in Peru for Machu Picchu tourists, but that's a few hours. Worth it though if you aren't hiking, as the views are spectacular!
There's also a train to the clouds tourist train from Salta, Argentina, but it's a one-day thing and comes back to Salta at night.
However, not to worry! The buses, especially in Argentina and Chile, are absolutely fantastic! For example, a trip from Santiago to Iquique. They inevitably have movies, great seats that for a few extra euros you can convert to seats that become beds (known as full-cama), and can get food options from crackers up to roasts!
Bolivia and Peru weren't quite as luxurious, in fact I found the buses in Bolivia painful (but they were cheap), although near Lima in Peru you could find the full range of luxury if you so wanted.