The resolution of a given instrument is proportional to its diameter, and inversely proportional to the wavelength of the light being observed. Diffraction effects are the main contributors to this limit.
Most telescopes on the Earth ground work at a much lower resolution than diffraction-limited, because of the distorsion introduced by the atmosphere. Some of them have recently started using adaptive optics technology, resulting in higher resolution, but it's still difficult to reach the diffraction limit. Radiotelescopes are better in this regard, because the wavelengths they use (from millimiters to meters) are so long that the atmospheric distorsion is negligible.
Space-based telescopes (such as the HST, or a number of non-optical telescopes) always work at their diffraction limit.