When you wake up on July 10, SQL Server 2008 and 2008 R2 will be out of support. Microsoft has been talking about this for some time, there's been a Migration Tour from PASS with live events in quite a few cities, webinars, and more to let you know that you might want to upgrade to a supported version.
While I typically think that systems that run are fine and don't necessarily need support, there are compliance and security concerns here. If you work in a regulated industry, you might need support to stay compliant. If that's the case, you might want to ensure you have plans to move to SQL Server 2017 (or 2019) soon.
The same goes in this era of attacks and potential security issues. While SQL Server has relatively few patches for security, you never know. I haven't worried about this in the past, often with internal servers, but I do get more concerned over time as we seem to constantly find more complex bugs in hardware and software.
SQL Server 2008 support is over, but you have options. Microsoft will continue to support you if you move your servers to Azure. That's not a bad option if you need to move quickly, but don't forget to really think through what this means for your applications. Moving to Azure isn't necessarily as smooth or simple as you might think. Authentication and authorization need some attention to detail to get working well. It's not hard, but it is work.
When SQL Server 2005 went out of support, it didn't seem there was as much emphasis on migrating. Certainly lots of people ran SQL Server 2000 instances for many years without support. You can do it, but the world feels more dangerous, and there are more implications with regard to regulation, security, insurance, and other complex topics that can impact your business.
Think carefully about the implications of migrating and not migrating. You'll have to make the decision, and it can be hard, but it's something you should spend quality time thinking carefully about.