In the end, not really. You have to have SOME kind of Verizon set-top box to decrtypt the vast majority of your HD channels. Another, probably spendier alternative is to buy a TiVo box and pay THEM a monthly service charge AND rent a cablecard from Verizon to boot.
If you only care about recording your local SD and HD channels (which are not encrypted) then you can purchase a DVR with a QAM tuner and plug the coax directly into that. I believe something like HDHomerun is another option: http://www.silicondust.com/products/hdhomerun but I don't think it records in full HD resolution...
Around here we have two HD (non-DVR) set-top boxes from Verizon that are each connected to two different PCs (one with a TV tuner and another with something similar to a Slingbox) and we each record via Media Center. I'm probably going to get Hauppauge's newest HD PVR (full resolution HD recording) shortly after the new year, if not sooner... it will still need an HD set-top box though, to get all our HD channels.