yes if you're just riding to the shops or doing footpaths, but no if you intend to jump 20ft gaps or do 10ft drops as we were doing yesterday (small for some people, big enough for me having not ridden much for a couple of years).
'proper' downhill bikes have 8-10 inches of travel on them these days and whilst i find them a bit overkill for most uk courses, they have their place on some and come into their own in the french alps at summer time. it's a whole different sport to what most people think of as mountain biking.
mind you mine can happily be used for normal riding too, in fact i was rather pleased at how well i could ride back up the hill after, laughing at my mates on big bikes.