The Mac Pro 4,1 (2009) can be flashed to a 5,1 (2010-2012) and should be able to run the latest MacOS and software for at least a few more years. These machines have a greater longevity that many others.
That said, if you have a Mac Pro 3,1 (2008) the latest version of OSX officially supported is El Capitan 10.11.x though there are patches in the words to get Sierra 10.12.x to run on it.
I recently put an SSD in my 3,1. That alone has boosted performance significantly. I will be doubling the existing 8GB of RAM to 16GB, and if prices remain reasonable I may eventually fill it up to 32GB as finances allow. The bottleneck in the system now is the RAM, which is only 800MHz. DDR3 and DDR4 are now often 1600MHz or 1866Mhz, and some high-performance stuff is now over the 2GHz clock speed.
From what I am reading, the Mac Pros after 2008 are a bit harder to upgrade since the heatsink bolts also form the CPU retaining mechanism and it is tricky to get it right when you upgrade the CPUs. If I buy a newer Mac Pro, it will be something from 2010-2012 with the highest-rated CPUs pre-installed and I won't touch them after that.
If it is a speed enhancement that you want, you are probably best looking at some sort of PCIe SSD for the boot drive and retaining the SATA for storage drives. If you've got money to spend, you can get some large capacity SATA SSDs and RAID them for best speed. I would probably keep a mechanical HDD as a back-up drive. On my own set up, while I have set the SSD as the boot drive with all the applications, I have a complete installation of OSX still on the 1TB HDD in case the SSD fails.
The fact with computers is that they eventually become obsolete no matter what you do with them, so think about the cost-benefit schema. If your 2008 Mac Pro is going to be useful for another 3-4 years despite no official support for Sierra, then I say run with it. Chances are that there will be very few programs that require anything newer than Yosemite for a while anyway.
It may be the case that the Mac Pro gets retired from the high-end "pro" work and becomes an office desktop machine - a job which it should continue to do well for several years. Admittedly, 90% of the work that I do with mine is with an office suite and internet browser. As long as MuseScore and GarageBand continue to work well on this system, I'll hold onto it.