That kinda depends.
I'm of the school that routes all video sources directly to the monitor and uses that for video selection. Along with that, I also route the primitive red/white analog outputs from the sources to thecorrosponding input on the TV.
Also, I run the "better" audio (digital coax, toslink) directly to the receiver and use that for audio selection/switching.
This allows me to select a source via the TV, watch the source on the TV, have rudimentary audio through it's internal speakers and not even turn on the receiver. I don't need a cooking show, the grandkids purple dinodsaur/Bob the Builder videos, or the daily news in 5.1 surround. Those little speakers are fine for that.
But, when I want the big sound, I turn the volume down on the TV, turn on the Denon, select the source, and blast away. All is right with the world.
Heck, many times I have the kids sitting (duct-taped together) watching a video and I'll be sitting in the LazyBoy listening to a CD with my headphones on. Who says I'm not a good Grandpa?
So, if you intend to route everything through the receiver, then HDMI becomes important. As it is, for myself, I don't find it really necessary at this time.