AFAIK, all RNAV SIDs in the US (FAA AIM Chapter 5-2-7.f) and Europe, plus numerous other places, require RNP-1. If you know of any exceptions (US/Europe), please post them.
Also, an airplane must be certified to RNP-1 to operate on SIDs/STARs that require RNP-1. If any of its systems are degraded or inoperable, the DDPG must be consulted to ensure the RNP-1 certification remains valid. For example, the 744 requires 2 IRUs and 2 FMS/CDUs operational for RNP-5.