Ever see the "feet" that you place underneath plant pots in your garden? The purpose of those feet is to allow water to drain away, without them the pot will remain wet/damp and when the temperature drops below freezing in winter the pot will crack. Water has that effect on terracotta, clay and even concrete, especially thin concrete such as roof tiles.
Moss holds water, so by removing the moss from the roof you are reducing the possibility of tiles suffering from winter cracks. Moss also tends to grow on cement, so it can disturb the bond between ridge/apex tiles and the roof.
By itself moss wont damage the tiles and the biggest advantage of a moss removal project would be on the guttering. With less blockages they can work more efficiently and require much less maintenance. The chances of an expensive blockage in the underground drain are reduced and products such as gutter guards and down pipe filters will not clog up so quickly.
If you have excess roof moss and you are concerned about the tiles never having the opportunity to dry out, then yes removing the moss and preventing regrowth with chemical moss killers is desirable. If the growth is only mild then it may not be needed. It depends on whether you are fed up with constantly having to clear out the gutters or seeing clumps of moss on your lawn/patio.
Tips for roof moss removal:
Use the correct access equipment - safety first
Carry out this type of work when the roof is dry
Start from the top of the roof and work downwards using a trowel to scrape off the moss
Using a stiff broom sweep off any loose moss and dust
Replace any broken tiles and clear out gutters
Check condition of cement work and repair as required
Spray roof with a fungicide moss killer to kill off any roots and prevent early re-growth
Should I use a pressure washer?
Using a pressure washer is one way of removing the moss along with any other dirt and grime. However if you have broken tiles on the roof then there is a flood risk and old tiles can suffer from discolouration as the loose grit on the tile surface is blasted away. Most professional roofing companies tend to stay away from using pressure washers, so that just leaves the cowboys and questionable firms.
Moss will probably not damage the roof. Moss tends to grow on the surface of the tile feeding on minerals and grime that collects on the tiles. In most cases moss will not damage the tiles, however there will always be corner cases and older tiles are more likely to suffer problems.