In the spirit of asking a Good subjective question I bring this forth again, in hopes that ServerFault will continue to be a preferred "go to" when searching on this topic.
OLD REFERENCE
Back in 2011 this question was asked: Reasons Why In Place Upgrades Are Bad
THE QUESTION
Is doing an in-place upgrade of Windows Server x64 (2008 R2, 2012, 2012 R2) to a newer supported Windows Server version a good practice these days or no?
THE ANSWERS
Remember from the link above: Great subjective questions tend to have long, not short, answers. The best subjective questions inspire your peers to share their actual experiences, not just post a mindless one-liner or cartoon in hopes of being rewarded with upvotes for being merely "first."
My opinion is, when supported, an in-place upgrade of a Windows Server OS to a newer version is the preferred method for upgrading a server (especially a VM) these days. Not only is it much quicker, and allows for greater automation, but it also no longer holds as much risk vs. reward that older OS in-place upgrades represented due to Microsoft's support of a better lifecycle transition model.
Microsoft has done a lot to make sure that in-place upgrades are easier than before and more seamless, without the problems that plagued older OS upgrades. This seems to be the recommended course of action if you want to keep everything as is: Windows Server Installation and Upgrade:
Even MS bloggers are believing the hype: In-Place upgrade of 2008 R2 to 2012 R2
In addition, VMs allow for snapshots, P2V, cloning, and rollback to ease in this transition. (Reference: "P2V it into a test VM and, uh, test it."
We should be "Treating servers like cattle not pets" - Randy Bias. The old days of caring and feeding the servers you are responsible for isn't done as intimately as it once was. Not every server is a snowflake, and public cloud hosting is a prime example of this practice.
For instance:
I've personally done multiple in-place upgrades from 2008 R2 to 2012 R2 over the past year, with about 400 more planned for the next year and a half. All have gone just fine, with only minor issues afterwards on 2 servers that didn't require rollbacks. As long as the existing server is running fine, you should feel confident in moving this direction.
Some important things to consider when making this claim that in-place upgrades are the preferred way to go:
Is the existing server running well currently without issues?
If the answer is YES to ALL of the above questions, then an in-place upgrade is the preferred route.
Just for on-going reference, and to add detail straight from the horse's mouth from a more recent article, Microsoft does not support Azure upgrades. Cattle are killed, not upgraded.
I would like to point you to Microsoft's Office 365 fundamentals course. They explain how Microsoft stamp out a bunch of server with automated build processes. They don't upgrade or even patch them, they just stamp out another bunch of servers using automated deployment tools. Automation is king and I need to get better at it.