A lot of seismology veterans are completely jaded from the failure of the Parkfield experiments to turn up any precursors. I'm new to the field and young, so understandably I'm more optimistic.
In my opinion, there are clearly some precursors to some earthquakes. There is a huge variety of precursors to choose from for any given fault.
1. Seismic gap. Some faults signal an imminent earthquake by a sudden drop in seismicity: suddenly there are no earthquakes; that means the fault is not moving, not releasing stress, and when it finally does move, it'll move a lot very quickly.
2. Small strain. The Tohoku region supposedly had relatively small strain rates from GPS data (i.e., the land wasn't deforming very quickly). Some Japanese seismologists argued that the results meant that the fault was locked and still building up stress, and yet others argued that the fault was simply not that active, anymore. The seismologists arguing that the fault was locked and would give way to a huge earthquake proved to be correct. However, the strain rates would have been small for hundreds of years. Saying there's going to be an earthquake sometime because this fault is not moving much is not much better prediction than we can do now.
3. Electrical current/resistivity/ionosphere charge. This kind of thing has been reported for so long that I'm certain that it's a real phenomena. People throughout history took notice of "earthquake lights" before an earthquake. Scientists never believed them until the Japanese actually took pictures of earthquake lights several decades ago. People have also reported seeing strange lights floating above the ground, strange cloud formations, and spikes in ionosphere charge seem to happen frequently enough. The sharp current in rocks immediately before fracture (NASA scientist) is also promising. None of these things are very reliable, though;
4. Gases, ground water changes. If as my adviser said, that snakes wake up from hibernation due to some kind of gases is true, that surely shows some leakage of gas from the ground before an earthquake. If I recall, there is also Japanese folklore discussing strange smells before earthquakes. I believe earthquake cloud people also claim that some escaping of gases contributes to earthquake clouds. And there have been many studies about well water depth and composition changes before earthquakes.
5. Stress buildup and recurrence. There are many earthquakes that occur periodically. We can see that the Great Tokai Quake in Japan occurs every ~150 years and it's been 156 years since the last one. We can measure the stress buildup on the fault and say, "if this whole fault goes, there will be a M8.X earthquake." However, despite how obvious this method is, it's also woefully unreliable. The Parkfield earthquake happened every 20 or so years for as long as people have lived in California, and only the past one was 20 years late (and with no precursors).
In my opinion, there are a lot of different precursors that do happen, but don't reliably happen. But before I entered seismology, I seriously considered meteorology. To me, predicting an earthquake is not too much different than predicting a tornado, albeit more difficult. For tornadoes, we use radar to measure particle velocity in the clouds, and issue warnings after some set of circumstances has been fulfilled. If there is strong rotation or a wall cloud, there is a tornado warning. Despite the clear understanding that tornadoes form from strong downdrafts in strongly rotating thunderstorms and supercells, and they most frequently drop from wall clouds, not all rotating wall clouds produce tornadoes. In fact, most wall clouds do not produce tornadoes. We haven't given up predicting tornadoes, though, and we certainly don't regard tornado warnings as useless. We just accept that most tornadoes happen when there is a rotating wall cloud, and sometimes, but rarely, tornadoes will happen outside of expected circumstances that we can't predict.
Perhaps we should rethink earthquake prediction; it needs to have more public and engineering involvement. I think that it's inevitable that someday in the distant future we will be able to say "circumstances are prime for an earthquake", and be able to issue some kind of earthquake watches or warnings, just like the weather. But a tornado watch doesn't mean that everyone should worry and get ready to run to the basement, and a tornado warning even doesn't mean that we should panic, stop what we're doing, and run to the basement (although we should get ready to do so). Buildings should be strong enough to not collapse, and people should be confident enough of their buildings that they can hide under a table and be safe. An earthquake warning would mean, "we don't know if an earthquake is going to strike, but if the earthquake alarm starts sounding, let's remember what we practiced in our earthquake drills." It wouldn't mean that everyone should camp outside for a week until danger passes.
A lot of the older seismologists are simply jaded from over 100 years of unsuccessful earthquake prediction, and especially that we are still unable to predict them even after the explosive growth in understanding of earthquakes of the past 50 years. I think we are trying too hard to do the impossible and need to work harder on what we can do. We should accept that there are many possible precursors, of which any given earthquake may or may not exhibit. Some will exhibit multiple, and others will exhibit none. We should accept that some earthquakes will be unpredictable and move on; we shouldn't abandon prediction of all earthquakes. In addition, I think we should strive to change the notion of an "earthquake warning" from "everyone run out of the building and camp in tents for a week" to "be prepared to seek shelter should your earthquake alarms start sounding." We also need to work on good earthquake alarm systems such as Japan's UrEDAS and Earthquake Early Warning (EEW) systems. Seismologists should be able to say, "this area that we expect an earthquake in is exhibiting possible precursors X, Y, and Z. If the whole fault ruptures, we know it will produce an earthquake of magnitude X due to the stress that has built up on the fault since the last quake. Be prepared to seek shelter." Politicians need to work to keep people from panicking from such a warning; instead we should be prepared. We should not be prosecuting seismologists for failed warnings or the lack of a warning.