I have this problem and I have tried these possible solutions without effect:
Reinstall Mavericks
Reset SMC
Reset Pram
Change Headphones
Change interface (problem occurs on integral soundcard as well as on my USB interface)
Change output format (2ch 32bit float, 24bit integer, 20bit integer, 16bit integer)
Mute all other outputs in audio/midi setup
Reset sound card using "sudo kill -9 `ps ax|grep 'coreaudio[a-z]' | awk '{print $1}'`" in terminal
Some things I have noticed:
1. Since the problem started happening, I can adjust volume with volume buttons on keyboard even though I have plugged in my USB interface. Before the problem started, I was given the 'forbidden' sign when I pressed these buttons.

2. I remember changing sound output to mono one time when I only hade one speaker, and I can't remember the problem occuring before that time. This can possibly be the point when the echo started. The problem now happens both in stereo and in mono.
3. The echo seems to be more present in the lower frequency band. The more bass in the sound played, the more echo is heard.
4. The echo does not happen when playing "mac sounds" like the change volume sound or "sound effects" in sound preferences.
5. The echo does not happen when using speakers, even though it's the same output jack (both integral and USB interface)
Any help is greatly appreciated, I depend on my headphones working properly in my work!
(excuse me if my english is somewhat incorrect, I am from Scandinavia)