This is from one of our servers at work. Sadly, I'm in the process of decommissioning it now and will have to shut it down in about two weeks.
Nice, you beat me. Had a dedicated Debian server reach 4 years of uptime a while ago. The motherboard eventually died and the hosting company (OVH) replaced it. I took me a few minutes to understand why the thing wouldn't boot back up: the Debian distribution was so old that it didn't recognize the network chipset on the new motherboard!
No critical kernel security patch came out during these 4 years so I never needed to reboot it. Now it's back at nearly 600 days up again. My other dedicated server is at about 500 days uptime. I installed many patches but none requiring a reboot.
They're not very critical stuff either: they're Internet facing but mostly used by devs so I'm not losing sleep over these.