With the aim of exploring the properties of the class of FR0 radio galaxies, we selected a sample of 108 compact radio sources, called FR0CAT, by combining observations from the NVSS, FIRST, and SDSS surveys. The catalog includes sources with z$leq 0.05$, with a radio size $lesssim$ 5 kpc, and with an optical spectrum characteristic of low-excitation galaxies. Their 1.4-GHz radio luminosities range $10^{38} lesssim u L_{1.4} lesssim 10^{40}$ erg/s. The FR0CAT hosts are mostly (86%) luminous ($-21 gtrsim M_r gtrsim -23$) red early-type galaxies with black hole masses $10^8 lesssim M_{rm BH} lesssim 10^9 M_odot$: similar to the hosts of FRI radio galaxies, but they are on average a factor $sim$1.6 less massive. The number density of FR0CAT sources is $sim$5 times higher than that of FRIs, and thus they represent the dominant population of radio sources in the local Universe. Different scenarios are considered to account for the smaller sizes and larger abundance of FR0s with respect to FRIs. An age-size scenario that considers FR0s as young radio galaxies that will all eventually evolve into extended radio sources cannot be reconciled with the large space density of FR0s. However, the radio activity recurrence, with the duration of the active phase covering a wide range of values and with short active periods strongly favored with respect to longer ones, might account for their large density number. Alternatively, the jet properties of FR0s might be intrinsically different from those of the FRIs, the former class having lower bulk Lorentz factors, possibly due to lower black hole spins. Our study indicates that FR0s and FRI/IIs can be interpreted as two extremes of a continuous population of radio sources that is characterized by a broad distribution of sizes and luminosities of their extended radio emission, but shares a single class of host galaxies.
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