I don't think DX10 is gonna be mandatory for anything developed outside of Microsoft for quite some time until Microsoft gives up and releases DX10 for XP. The attach rate of Vista is pathetic and many stores are packaging new PCs with XP again due to people avoiding the Vista boxes.
And to answer your actual question, you will be able to run a lot of new games just fine, but most modern games are leaning so heavily on HDR lighting, AGEIX physics, and other new fancy effects that absolutely require 3D card support, to the point where the game looks like trash without these options on (see: Oblivion).
If you already have a dual-core processor, you probably only need to upgrade your video card, and there are tons of good ones in the $200 range.
http://www.newegg.com