Digital photography has come a long way in the last few years. Few today would argue that digital cannot stand as film's equal. In many cases the technology now surpasses film. Not only do we have a digital substitute for film, we also have digital substitutes for most physical filters. Between the built in tools in Lightroom and the many sets of plugins available there are really only two physical filters needed today.
The effects of a polarizing filter cannot be reproduced digitally. Yes, there are a few digital polarizing effects which attempt to approximate some aspects of a polarizer. But only a physical polarizer present between the subject and the sensor can remove reflections and deepen the sky's shade of blue. You can get close with digital effects but it's much more work that just putting that filter on the lens.
Neutral density filters also have no digital replacements. Some aspects of contrast and tone can be simulated digitally. But there isn't a digital filter around that can cut the light on site and slow down your shutter speed. If you are out on a sunny day and want to slow your shutter for that dreamy cotton candy waterfall effect, the neutral density filter is your best friend. You can get a set of different density filters or a single variable density filter. Whichever you choose you'll eventually find yourself happy you have it in your bag.
I can hear you saying, "OK. I have those filters. Why do I need any more?" Well, you don't need any other filters. However, you may want to consider other filters. While it's true that you can easily recreate starlight effects on highlights or selective focus techniques via plugins you can still benefit from a physical filter.
For example, let's look at the Lensbaby Composer. Not just a filter but a lens substitute, the Lensbaby lets you pull areas in and out of focus. That selective focus look can be reproduced via a plugin such as FocalPoint 2 from onOne Software. What's the difference? The plugin can give you excellent results but it can't help you see things differently in the field. The Lensbaby can help spark your creative vision by letting you see your world a little differently.
The same can be said of other creative effect filters popular in film days. Starlight and soft focus filters aren't needed anymore and can be recreated digitally. But sometimes seeing the world through a starlight filter reveals new and interesting perspectives. Creative vision is a funny thing. Sometimes it's fragile. Other times it is stuck in a rut. Small things can provide a spark to reignite it.
Don't misunderstand me. Digital filters are amazing and wonderful things. Many are capable of much more than their physical counterparts ever were. But our old friends can still inspire and show us new ways to see our world. Get your basic filters first. Then try an effects filter or two and see if they spark your creative vision.