Within Debian there are or have been four different ports to various flavours of the ARM architecture:
ArmPort - the first port, using the "old" (now obsolete) ABI (OABI). First released with 2.2 (Potato), last released with 5.0 (Lenny). GNU Triplet: arm-linux-gnu
ArmEabiPort - newer port using the "new" ABI (EABI), supported on ARM v4t and higher. First released with 5.0 (Lenny). GNU Triplet: arm-linux-gnueabi
ArmHardFloatPort - the latest 32-bit port, using the hard-float version of the "new" ABI (EABI), targetting ARM v7 and up. To be released with 7.0 (Wheezy). GNU Triplet: arm-linux-gnueabihf
Arm64Port - the latest port, for the 64-bit ARMv8 architecture. Likely to be released with 8.0 (Jessie). GNU Triplet: aarch64-linux-gnu
Outside of Debian, a notable unofficial port to EABI ARMv6 with hard float is Raspbian, designed for use with the raspberry pi.