Historical
Look at tape delays - Watkat/Roland RE201 Space Echo
Digital Delays - Korg
Plug Ins - Logics Tape Delay/Stereo Delay/Delay Designer
Parameters
Delay Time - Time between repeats. Usually measured in milliseconds on analogue units. Plug ins may have tempo sync option where delay time is measured in musical divisions and locked to sequencer tempo
Character - Allows you to filter out frequency content of repeats. Hi Pass will progressively filter out more and more low frequencies from each successive repeat. Low Pass will progressively filter out more and more high frequencies from each successive repeat (this emulates how real tape degrades over multiple playbacks)
Feedback - This determines how many repeats will happen. Lower values means less repeats that will gradually fade out. Higher values will give more repeats. 100% means repeats will continue indefinitely. Values over 100% means delays will gradually increase in volume.
Dry/Wet Mix - allows you to balance volume of incoming signal against volume of echoes.