A few weeks after my 6/13/07 surgery for a cementless ReCap metal/on/metal resurfacing with Dr. Gross, I experienced "clunking". Many hip patients have this or something similar. For me, it was painless, but felt like during some movements the movement would feel resistance, then a pronounced snap as it gave way and the movement continued. The idea of a tight tendon moving over a protuberance and getting momentarily impeded, then giving way, felt like what was happening, although I couldn't figure out what tendon was doing it, or what exactly was doing it or what I could do about it. Surface Hippy has many accountings of similar occurances, but to this day - August 2010 - there are still only guesses and anecdotes as to what's going on. Seems like something so common should have been figured out by now. I'm going to assemble what I've been able to discover and put it on this page, both for my own reference and others.
This ref says it's commonly due to either the iliopsoas tendon or the iliotibial band. During running post-surgery, I've had iliopsoas tendinitis develop, and also IT band syndrome develop - so this sounds promising. The IP tendinitis link says that "snapping" commonly goes with this IP tendinitis. Now, to figure out what is snapping over what and so hopefully self-diagnose with more confidence... For me, standing with weight on both legs, I slowly move side to side, slightly shifting my weight, and putting my hand on the front of my left hip, the snapping clearly isn't happening here. That seems to rule out the iliopsoas. However, I notice that the psoas goes right over the front of the hip capsule since it attaches at the lesser trochanter. Could the IP have been cut or injured during surgery and was re-attached and is shorter now? Just speculation at this point. Joined by the iliacus, psoas major forms the iliopsoas which is surrounded by the iliac fascia. The iliopsoas runs across the iliopubic eminence through the muscular lacuna to its insertion on the lesser trochanter of the femur. The iliopectineal bursa separates the bone from the muscle at the level of the iliopubic eminence. The iliac subtendinous bursa lies between the lesser trochanter and the attachment of the iliopsoas. 
Google Images for 'snapping hip syndrome'
IT band "snapping" happens over the greater trochanter - that knob of bone on the outside of your upper femur. It's apparently quite "visually evident" even from across the room. I've had IT band soreness develop with running, although not this year. And my "snapping" feels much closer to the hip joint itself and not the IT band/greater trochanter area. Placing my hand over my greater trochanter, same - no snapping, so it's not the responsible tendon either.
On SurfaceHippy, one 5 year resurf veteran says her snapping stopped after proper exercise of the small muscles around the hip. She had success with "clamshells". Here's her advice...
"Not sure if I have a solution but this is what my excellent PT told
me and what
I worked on which resolved my clunking...finally. We active adults that do a
lot of things, think that those things like you mention below should be enough.
But what my PT told me is what many of us fail to do is work on the tiny muscles
and soft tissues around the hip joint. So, do clamshells AND side straight leg
raises, BUT here's the clincher, lay on your non operated side and raise your
operated leg ONLY about an inch from the other, do that for 3 or 4 reps, then
raise it about 2 inches for several reps, then 3 inches, etc. TINY little
movements. Same with the clamshells. Those are when you lie on your side with
your legs bent and you raise your knee, open and close like a clamshell looks.
Just follow that except do not raise your knee that high, do little tiny
movements, start off only an inch apart for several reps, etc. Hopefully that
will help, I know that I have not had the clunking sensation now since two years
Sept 2012: Found this good site on soft tissue injury around the hip, and rehab using massage and stretching, including "snapping hip syndrome".
My Symptom progression
The snapping hip syndrome came on early in my recovery and remained for many months, gradually disappearing. However, in January '13 it has returned, and i believe it also has made a mile brief appearance or two perhaps at another moment in the past few years, but not enough to have had me comment and record it. But now, in Jan '13, it has returned, and also pain on running that is being difficult to get rid of, after a heavy start to '13 with 40 miles of running in the first 15 days - now I'm sidelined, and have 'snapping hip' and pain that is felt at the top of the IT band right at the hip socket on the outside when I put weight and forward motion on the joint. It's certainly improved with the time off, and I have biked for plenty of miles w/o trouble, so it's not scary.... yet. The snapping, however, is definitely coming from right at the hip, not outside where the IT band is. I feel it's two separate issues. I'm also feeling pain around my hip socket when I run any length of distance, even just a mile. It slowly aches and gets worse until I slow and then can't run any longer, and it remains for a few days. It doesn't hurt with normal walking, once I lay off.
The iliopsoas tendon 'snap' happens over the femoral head itself, in this diagram. My feeling - I could easily believe this is my situation. Perhaps the femoral metal piece is slightly larger than the original femoral head? Perhaps the metal/tendon rubbing has irritated the tendon? A conflicting fact - the measurement of the 'tightness' of my psoas shows it's normal, not tight. Now, does it need to be extra loose just to avoid the 'snap'?
WebMD says one source of 'snap' is the rectus femoris tendon snapping over the femoral ball. Could this be me? Both the IP snap (below), and the RF snap happen over the femoral head (is there really room for BOTH to go right over the femoral head??), which is where it feels like it's happening.
Rectus femoris stretch #1
This image seems to indicate a pain location right where I'm feeling it; as the RF goes over the femoral head.
Links worth reading on snapping around the hip.
Dancer's hip snapping
Snapping hip syndrome and relation to illiopsoas tendinitis
psoas stretch images