Your Mac is already eight years old, next year it will be nine years old. In both dog and computer years this is ancient. Despite this it can still run the current most up-to-date version of OS X and hence run nearly all current applications.
As dialabrain says there is no way to predict whether Apple will allow your model Mac to run the next version of OS X - presumably 10.12. Even if it cannot it will still run current applications. With it being currently eight years old you have already got your moneys worth out of it. As it happens the annual World Wide Developer Conference takes place next week and this might reveal which older model Macs will be able to run the next version of OS X.
You do not detail your Macs current specs. e.g. how much RAM you currently have so we cannot judge what area is best to upgrade but it is possible to add more RAM, and it is possible to fit an SSD drive which it can boot from. In fact most Mac Pro models are fantastically flexible in terms of upgrades. I have upgraded the video card, CPU chips, WiFi, Bluetooth, and fitted an SSD to mine, and more recently just added USB3 as well.
Note: Your model being a 3,1 uses the older 'Fully Buffered' type of memory which is more expensive and I suspect harder to find. You could consider selling your Mac and getting a newer even if still second hand model.
This may be helpful in deciding how upgradeable your current Mac is - http://www.everymac.com/systems/apple/mac_pro/specs/mac-pro-eight-core-2.8-2008- specs.html