I appear to have mushrooms growing in my fortress, should I be worried about this and if so how should I deal with them?
No, mushrooms are not dangerous but can be a nuisance.
Mushrooms are the underground equivalent of plants. Smaller mushrooms are collected with the Gather Plants designation and can be a source of alcohol, food and/or cloth, depending on the species. However, they're not that interesting- they're available when you embark and you've probably been cultivating them for a while.
Larger mushrooms are the equivalent of trees and can be cut down by woodcutters. They are a source of wood, sometimes in unusual colours. They're not dangerous but they might get in the way if they're growing in the middle of a corridor or a room.
Mushrooms will grow in any underground muddy area, i.e. any soil or areas of rock that have had water on them. To remove the mud, build a floor over the muddy area.