A pal of mine recently asked me for a recommendation on delays for Live. I made a point to recommend my favorite 3rd party option (Dub Machines by Surreal Machines) but I also told him that I use the stock ones a lot, since they're pretty powerful when you start to tinker with them. Here's 3 quick tips on using the built in delay sounds in Live.
Repitch Mode = Vintage Analog Delays
Like many of the other effects in Live, right clicking the header of the delays reveals some advanced options under the hood. The Simple, Ping-Pong, and Filter Delays all have alternate engines that can be engaged via this method.
1. Load any of these 3 effects and right click the header
2. By default, delays are set to "Fade". This behavior means that when you change delay times, a gradual transition is made with a crossfade between the old and new times. By changing the selection to Repitch, changing the delay time also changes the pitch, which is how classic tape delay machines like the Space Echo operate. To hear this best, drop a fully wet delay on a return and route some of your snare there. Then start to play with the delay time, unsynced. You'll hear some familiar and amazing dub effects that can be used on any sound.
Gated Delay = Polyrhythm
Sending snares and hats to a simple Ping Pong Delay return can quickly add some polyrhythm to your drums. To add some additional spice, place a gate right after the delay and set the threshold so that it cuts off the delay half way through. You'll get a shuffling effect overtime the gate opens and closes. Check out this quick video to see what I mean:
Automation = Feel/Vibe
One of the best ways to use delay is to automate it. Using the "Device On" automation lets you program when the Delay turns on and off, cutting the trail completely. A great way to make a single word or instrument solo stand out is to a turn the delay off during the word or element you want to emphasize. You can also mute the delay right before a hook and then reintroduce it so the sound expands during the hook and gets "bigger". Automating the delay time is a great way to do this too. Try automating different times for different parts of the song to emphasize changes and shifts.