They do not alias so are kind of important in front of ADCs (And are a vital part of correctly reconstructing DAC outputs)....
Up in the RF they are more then somewhat important for building radio systems, everything from cell phones to TVs needs both RF and IF filters and of course transmitters need filters to comply with the out of band emissions regulations.
The art of designing high performance radio systems is all about filtering out everything you dont need as early as possible, by the time you digitize signal bandwidths should be a fraction of those at the antenna input.
There are plenty of places where SAW, Crystal and even simple LC network filters are still the best way to solve a problem, and microwave filters designed as PCB geometry can of course have a really attractive BOM cost.
Then we have the fact that a filter can be designed to transform impedances, which can be a huge thing, and indeed you often see LC networks used primarily for this effect (They filter as well, but that is incidental).
Then of course we have unintentional filters, long power grid lines for example can have significant phase shift, and I well remember when grid stability was mostly rule of thumb....
73 Dan.