Many of the filters that were used 'back in the day' are obsolete in the digital era. It's just a lot easier and more flexible to apply those effects with software. For example, there is very little need for any color filters. You can easily adjust the colors in a digital image and you have infinitely more options that just filter on or filter off.
But that being said, there are still uses for filters with a digital camera. For example, the effects a polarizing filter can't really be replicated in post, so it can be a very useful filter.
Split or graduated filters can come in handy, because they can allow you to compress the dynamic range of a scene (as seen by the camera), which can allow you to photograph a scene that might otherwise have been beyond the camera's ability to capture. Although, with HDR techniques (multiple exposures) the need for grad filters is much less.
Neutral density filters (or any filter that blocks light) can be handy because they can be used to get a longer shutter speed for a given lighting scenario.