So my speaker in my combo broke and I want to replace it. I want to replace it with a Celestion Vintage 30 but I can only get a hold of a 16 or 8ohm speaker. The current speaker is 4ohms so I assume the output of the amp is 4ohms. Would I be able to put a 8ohm speaker in without damaging it?

The amp's impedance can be lower than the speakers and it'll still work fine.
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Quote by Axelfox
Assuming you have a solid state combo not a tube one the 8ohm speaker will be an easier load. The amp will give a little less power though. Whether you notice though will depend upon how loud the Celestion is compared to the old speaker.
Depends on your amp.  Some are far more critical about speaker load than others but since you have not told us which one you have we cannot give very useful advice.  

It might work.  
"Your sound is in your hands as much as anything. It's the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use." -- Stevie Ray Vaughan

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Guthrie on tone: https://www.youtube.com/watch?v=zmohdG9lLqY