Is there a good chance that gravitational waves will be detected in the next years?
Theoretical estimates on the size of the effect and the sensitivity of the newest detectors should permit a forecast on this.
Yes, most likely, unless there is something fundamentally wrong with our understanding of gravity. The most promising candidate for detection is Advanced LIGO, which is currently in the process of being designed and built. The website has some really interesting information listed, including the construction schedule (PDF), and the upgrades, such as upgrading from a 10W to a 200W laser.
According to Wikipedia, they are expecting to start operations sometime in 2014, which will be after they have completed construction and calibrated the instrument. Of particular note is that the higher power laser will make calibrating the mirrors more challenging, so right now they still have one interferometer (the shorter one) in operation and are performing a squeeze test. Once Advanced LIGO is complete, they are expecting a sensitivity increase by a factor of 10, pushing the detection rate to possibly daily.
It may also be good to note that they are still processing the data from the old data runs (by means of Einstein@Home), so it is still possible that a detection will turn up within the data, although it will be be of a different type.
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Yes, they expect to see a signal when advanced LIGO is up and running. Unless there is something supressing the Bh-bh, bh-ns and ns-ns merger rate, if gravitational waves exist (and the hulse-taylor binary makes this almost undeniable), then they should have a positive detection by 2020, unless there is something unknown modifying the way that gravitational waves propogate.