This thesis presents the results from a long-term timing campaign on 20 millisecond pulsars (MSPs). The stability of these pulsars is analysed in order to allow assessment of gravitational wave (GW) detection efforts through pulsar timing. In addition, we present a new method of limiting the amplitude of a stochastic background of GWs and derive a strong limit from applying this method to our data. GWs are a prediction of general relativity (GR) that has thus far only been confirmed indirectly. While a direct detection could give important evidence of GW properties and provide insight into the processes that are predicted to generate these waves, a detection that contradicts GR might herald a breakthrough in gravitational theory and fundamental science. Two types of projects are currently being undertaken to make the first direct detection of GWs. One of these uses ground-based interferometers to detect the GW-induced space-time curvature, the other uses pulsar timing. This thesis is concerned with the latter: the Pulsar Timing Arrays (PTAs). The high stability of some MSPs, along with ever increasing levels of timing precision, has been predicted to enable detection of GWeffects on the Earth. Specifically, it has been shown that if the timing precision on 20 MSPs can be maintained at levels of !100 ns during five years to a decade, a correlated effect owing to GWs from predicted cosmic origins, can be detected. However, no timing at a precision of 100 ns has been maintained for more than a few years - and only on a few pulsars. After combining archival data and employing state-of-the-art calibration methods, we achieved 200 ns timing precision over 10 years on PSR J0437−4715 - which is a record at such time scales. This high stability in itself provides several interesting measurements, for example of the variation of Newton’s gravitational constant and of the pulsar mass. We also present long-term timing results on 19 other pulsars that constitute the Parkes PTA. Our results show that most pulsars in our sample are stable and dominated by receiver noise. The potential for sub-100 ns timing is demonstrated on two of our brightest sources. These timing results are used to estimate timescales for GW detection of potential PTAs worldwide and to limit the amplitude of GWs in the data. Our limit of A < 1.0×10−14 for a background with ! = −2/3 is slightly more stringent than the best limit published yet.