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Hmm, if you drop a lens (it does happen!) it's usually the first element that gets broken and if you have a filter (such as UV or skylight) then that's far cheaper to replace!
However, it's important to use prime brand filters. So if you have a Nikon lens then get a Nikkor filter - No other will do! You don't put cheap brand tyres on a performance car do you.
A filter also keeps your lens free from inevitable grease, contaminents etc and is easier to clean.
Obviously a lens hood provides some protection, but.