I keep a clear filter on all of my lenses, where possible. These are high-quality multi-coated filters, B+W for the most part. I do this not to physically protect the front element from impact, but to keep the front element clean and avoid cleaning the front element directly, which can wear down the coatings (it's almost always much cheaper to replace a filter than replace a lens).
Of course, a filter introduces an additional optical element and corresponding air-glass interfaces that degrade image quality. A good filter will keep this degradation to a level that is not perceptible under normal shooting conditions. I explain this in more detail here.
Filters aren't the best option for protection against physical impact, although there are several well-known cases where a filter took an impact and broke where the front element could have sustained damage instead. If protection against impact is what you need, consider getting a lens hood instead. A hood shields off light that shouldn't be part of the image, increasing contrast, and extends the lens beyond the front element so that the front element is much less likely to be damaged on impact. A filter is useful for keeping the front element clean, but you'll need to decide whether this is worth the image quality trade-off.
However, some Canon L lenses with weather sealing (several non-white L lenses that are not internal focusing or internal zooming) require a filter to be installed in order to complete the weather sealing. For example, page 1 of the manual for the Canon EF 17-40mm f/4L USM lens states:
Since the front element of this lens moves when focusing (zooming), you need to attach a Canon PROTECT filter sold separately for adequate dust- and water-resistant performance. Without a filter, the lens is not dust or water-resistant.