Reason #1: It fixes a Denial of Service vulnerability.
Reason #2: It fixes another Denial of Service vulnerability.
Reason #3: It fixes an Open Source zlib vulnerability.
Reason #4: It fixes an Open Source libpng vulnerability.
If your users are running Notes 9.x for Windows, you want to upgrade them to Notes 9.0.1 FP9.
If your users are running 64-bit Notes 9.x for Mac, you want to upgrade them to Notes 901 64-bit Mac IF11.
If your users are running Notes 8.5.3 for Windows, you want to upgrade them to Notes 8.5.3 FP6 IF15. Then start preparing to upgrade your Domino servers and Notes clients to 9.0.1, because Domino/Notes 8.5.3 will be going out of support soon. You can upgrade your users to Notes 9.0.1 before you upgrade your servers to Domino 9.0.1.
If your users are running earlier than Notes 8.5.3, you want to upgrade them because you are running an unsupported version of Notes/Domino. Plus, the four vulnerabilities listed above are just the four most recently fixed vulnerabilities. Your old, unsupported copies of Notes harbor others too.
If your mail databases are hosted in IBM Connections Cloud or if you have implemented IBM Verse on-premises, you could migrate your users from IBM Notes to IBM Verse. But if you are running IBM Verse on-premises, I recommend that you upgrade your Domino mail servers to Domino 9.0.1 FP9. (I'll tell you why in my next post.)
And remember that, if you are hosting your Notes mail on on-premises Domino servers, your Notes/Domino licensing probably includes IBM SmartCloud Notes licensing. That means you can migrate your users' mail databases to IBM Connections Cloud-based Domino mail servers at no additional cost beyond your current licensing costs. If you are not sure what your Notes/Domino rights and restrictions are, ask me; I can help you to sort that out.
Also, if you don't think you can migrate away from Notes to Verse because you are still running Notes-only Domino applications, that's okay, because Notes is a great product. But if you would like to upgrade your apps, ask me about your options for browser-enabling your Notes applications. There are lots of options available.
Finally, if you are thinking about migrating from Notes/Domino to Exchange/Outlook or Office 365 or Google Apps or SoHo or whatever, ask me why you should reconsider. IBM Connections Cloud is superior to those other platforms -- runs circles around them, in fact -- in any number of ways. And it is getting better at an accelerating pace.
Addendum: I can help you automate (or at least streamline) your users' Notes upgrade process, so you don't have to babysit each upgrade.