I am currently using Ableton live with Augustus looper. I like loopers that are basically a delay with a hold rather than a “start/stop record” loop. The delays with hold are much easier to change over time –loops can transform and mutate into new loops. It is less fixed. This is sometimes called “feedback decay”
Ableton itself as a looper is very “start/stop record” that is why I use Augustus looper – you can also speed it up or slow it down and the pitch changes which is very cool! I use Ableton mainly for its routing capabilities and the ease with which you can set up remote control
Having a few Augustus Loopers that run in sync within Ableton allows separation of things like bass lines which can then come out on a separate output.
Before using software I used the Electrix repeater which is no longer available.
Here is a great video of my friend in New York, Brian Wolff demonstrating looping on the Tuba using two Electrix Repeaters
Back in the 1990s I used to make loops on the Digitech 8 second PDS8000. Very simple not very sophisticated but great fun. I sometimes still use it.
I used to play the trumpet through a Boss DE-200 Digital delay in the late 80’s early 90’s, and used this great machine to discover warbling modulating sounds and using the hold button to catch little phrases and noises from my trumpet. Getting the delay times in sync between this and the digitech above was always a challenge but produced great sounds
There are various internet resources for those interested in looping
Looper’s Delight – the first online resource and the best gear info up to 2005
Looper’s Delight on Facebook– discussion group
Livelooping.org – Methods ,tools, history and concepts
Looproom comparison chart – A quick chart comparing different loopers – up to date as of 2014