We can easily keep improving on the technology behind 3D printing, with faster techniques, cheaper materials and so on, and websites like Thingiverse will be critical to spread printable designs so that anyone can make at home whatever they want. However, after 3D printers become affordable household appliances and the materials are cheap enough to use on a whim, the biggest barrier will be designing the thing you need to print. So if you really want everyone to get into creating 3D objects, you need great 3D modelling software, available for free and very easy to use.
Mokalus of Borg
PS - Or a vast library of snap-together generic printable parts.
PPS - Like LEGO.