Narrowband images of 51 symbiotic stars were obtained at the ESO and ORM observatories to search for resolved optical nebulae. Ionized nebulae much larger than previously known are found around CH Cyg, HM Sge and V1016 Cyg, and they will be discussed in detail in forthcoming papers. A nebula with a deconvolved size between 0farcs9 and 1farcs5 is found around the symbiotic Mira H 1-36. The radio sources located few arcminutes aside of R Aqr (Hollis et al. 1987), which were suggested to be the remnant of a prehistoric eruption of the system, are found to be background galaxies. We also present a bibliographical compilation, updated to October 1998, of all the extended nebulae around symbiotic stars detected at optical and radio wavelengths, as well as a list of optical non-detections. The statistics of occurrence of these large ionized nebulae among symbiotic stars is discussed. Extended ionized nebulae appear to be a common component of the D-type symbiotics, and we infer that they are formed by the Mira wind and/or high velocity winds ejected by the hot component during outbursts. On the contrary, very few nebulae are detected around the systems containing normal red giants. Table 5 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html. Based on observations obtained at the 3.5m~NTT and 1.5m~DAN telescopes of the European Southern Observatory, and at the 2.6m~NOT telescope operated on the island of La Palma by NOTSA, in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofisica de Canarias.