Here's a neat idea for those lacking enough kitchen counter space. Instead of using a full-sized dish drying rack, create a vertical drying rack on the wall next to your sink using standard IKEA kitchen items:

According to Ikea Hackers, this vertical drying rack consists of a Bygel rail, two Bygel wire baskets and a Magasin cutlery caddy attached using S-hooks. If you're worried about pools of dripping water, just keep a towel underneath the rack. The only downside is that it won't fit a lot of large dinner plates, but is still great for cereal bowls, cups, small plates, etc.