Can't speak for mosses, but lichens are crucial pioneer colonisers of many habitats. Once established they can break down rocks to form thin soils which allow other plants to grow. If you have old wood (for instance fence posts), or stone garden walls then leaving these will often allow lichen colonies to develop.
The bushy lichens (like Evernia, Usnea) are used by many birds for nest building (although you're not likely to see these lichens in cities).
Under a microscope lichens host a whole range of small arthropods: typically various mites and springtails.
A number of attractive species of moth are lichen feeders: particularly noteworthy are the various species of Footman moths, the Marbled Beauty (a common moth in towns) and some of its close relatives. The larvae probably feed on lichens growing on roof tiles.
This page on conserving churchyard lichens describes quite a few of the standard do's and don'ts :
The British Lichen Society - Churchyard Lichen Conservation.
Lichens are very useful pollution indicators.
Broadly speaking keeping things too tidy or clean is bad for lichens (and often a losing battle). For instance pressure washing driveways gets rid of lichens (and other plants), but its amazing how quickly they return!
Sorry this is rather bitty, but hope if gives a flavour. I'm sure I've missed some obvious points too.