A router on a stick is a router with only one interface (usually an Ethernet interface). As far as I know, BGP route reflector are often router on a stick because they are not used to route packets but to distribute the BGP routes within an BGP AS.
Cisco offers a variety of Routers on Sticks :?: I have deployed a 3745 router with a NM 1GE card that trunked several VLANS to a Distrobution layer switch i.e. catalyst 6500 or 5500. In my current office we are running a 5500 with an RSM module. If you are looking to master the art of inter-vlan routing, pick up "CCNP 3: Multilayer Switching"
A Stub router, One-armed router or router on a stick is a router that routes traffic between virtual local area networks. It has only a single Ethernet NIC that is part of two or more Virtual LANs [VLAN], enabling them to be joined.
A VLAN allows multiple virtual LANs to coexist on the same physical LAN. This means that two machines attached to the same switch cannot send Ethernet frames to each other even though they pass over the same wires. If they need to communicate, then a router must be placed between the two VLANs to forward packets, just as if the two LANs were physically isolated. The only difference is that the router in question may contain only a single Ethernet NIC that is part of both VLANs (a one-armed router).