The U.K. is one of the very top tier countries on Earth. If other succession movements see it work in the U.K. than it will be a signal that it can work where they are at.
Also more immediate, if the Referendum passes you will see a secessionist/reunification vote in Northern Ireland faster than you can say "Ulster Scot".
Maybe Texas and some other states can secede... is Kansas with me or not? I like bread ya know.
If Scotland does make the break and then Northern Ireland begins a process of wishing to move away from English domination and unifies with Southern Ireland, becoming a full Irish Republic, it would leave only England as a monarchy in the area. This would in fact likely start a serious move to abolish the monarchy in full in England.
As it is, Australia is talking seriously about breaking away from the Commonwealth and becoming their own independent Republic. Then New Zealand is reputed to be making quiet preparations in breaking away from the Crown as well and becoming an independent republic. Thing is, Australia might do a great job, but New Zealand might not be a world power, but certainly, they would be determining their own future and that is more valuable than riches.