Even though Apple is claiming on their website that the new Airport Express can only act as a network range extender (signal repeater) with other Airport devices (look at the bottom of this page), WiFi Networking News's Glenn Fleishman explains why the Airport Express may just work with some non-Apple devices after all:
Wireless Distribution System (WDS) is a part of the 802.11 spec all the way back to IEEE 802.11b-1999. However, it was never made part of the Wi-Fi certification standard.
In WDS, each Wi-Fi gateway acts essentially like a port on an Ethernet switch. They broadcast information to each other about what adapters are available on their particular segments. If a packet arrives that requires a hop, it's repackaged and delivered to the right "port" or wireless gateways.
That is, if client A is attached to Base Station Z and client B is attached to Base Station Y, both Y and Z known about the clients on themselves and others. Packets flow from to A to Z, which repackages the packets using a WDS header, sends them to Y, which unwraps them and presents to them B as if they originated from themselves, more or less.
Because WDS isn't certified with Wi-Fi, no manufacturer wants to promise that their idiosyncratic version will work with anyone else's. However, because most of the 802.11g gear out there remains Broadcom based, the WDS implementation should be pretty similar.
Buffalo and Apple's equipment often works together, for instance. Linksys has chosen to use WDS as an either/or: either its WRT54G (for example) is a bridge or it's an access point. Apple and Buffalo allow either/and/or: you can make a base station a bridge (for Ethernet connected devices), a gateway, or a bridge and gateway.