A few times this week I have heard a buzzing sound coming from my monitor. It sounds like when a fly goes into one of the light killer things. Is it safe to use it till it dies or should I get my old spare out? Nothing else seems wrong with it.

http://forums.pcper.com/showthread.php?469454-Buzzing-from-monitor

If you dont have a warranty, you can probably still continue to use it, but dont look surprised if your monitor will go black someday.
Fixing stuff inside can be done but it is very difficult and usually not worth your time or money.

Which type of monitor is it ? LCD,LED,IPS

If its lcd, it could be the backlight buzzing.

If you go into monitor settings and turn turning the backlight (or Contrast, brightness) down, does the buzzing get lower in volume ?

It's a Hannsg HZ281HPB / 28 inch / Widescreen / LCD Monitor

It's only buzzing once or twice a day. It's not a constant thing

Sounds like the monitor is dying. It might last another year, or it might go -poof- tomorrow. Nothing you can really do but wait.