After a bit of drama that happened two weekends ago, I can now answer this question in the above photographic form. Don't worry - the lens in question has since been repaired and was only broken for a grand total of about 4 days!
From a little bit of googling it looks as if there is a bit of a heated debate around this topic, but I figure that I'd share my view (and now, personal experience) on it all.
USE THEM!
Having a UV filter on my 135mm lens has saved me a huge amount of hassle and expense.
My camera bag wasn't closed tightly enough and my lens fell out of it from a height of around a metre onto a concrete paving slab. As I am sure you can imagine it was one of those heart-stopping moments.. an "I need to look and see what has happened but I am not sure if I want to!" moment.
To my relief, the lens cap and filter absorbed the impact entirely. I quickly tested it by focusing on things at different distances and it appeared to be in full working order. Using a UV filter has saved me from having to shell out for an entire new lens, or the cost of having the front element repaired by Canon.
There are many, many tutorials online on how to remove bent and broken filters from lenses, but as I wanted to be 100% sure that my lens was in working order internally and not likely to fail on a client shoot, I did send it into Canon for a check up, and whilst it was there, have the broken filter removed. This came through at a fixed price repair (under £100!) and was most likely significantly cheaper than having it repaired had the front element smashed to bits instead.
There is a lot of debate online with regard to whether photographers should use filters or not to protect their lenses. The main argument is as follows: adding filters to lenses can slightly affect image quality. By investing in good quality filters (I use, and have always used Hoya PRO-1 filters), you can minimise this but there may still be a slight reduction in quality.
However, in my situation, it's more important to me that my lenses sustain less damage upon impact and be cheaper to repair, than having them filter-free and have images that are maybe possibly potentially slightly minutely sharper. Just my two cents!
What are your views on this topic? Do you use protective filters on your lenses?