The following working implementations exist at this moment. Most are under very active development..

Cisco: IOS / IOS-XR / NX-OS

Suitable for most Cisco ISR, ISRG2, ASR1K, Nexus 7000, Cat6500, and ASR9K  Routers

lisp.cisco.com   (A and AAAA) and  www.cisco.com/go/lisp

OpenOverlayRouter: openoverlayrouter.org (formerly LISPmob)

Runs on Linux, OpenWrt, Android and iOS

AVM/Fritz!Box: AVM Fritz!Box 7390

Runs on AVM Fritz!Box 7390 (firmware here)

Lispers.net: www.lispers.net
OpenLISP: OpenLISP.org

Runs on FreeBSD

Aless: Linux 2.6 implementation

Includes iproute2-lisp and lispd

LANCOM Systems: xTR implementation