There is no regulation to cover minimum crew when flying privately, other than as required by the airplane manual.
For commercial flights it gets a bit more complicated and the answer is, well, "it depends".
In EASA comercial flying the minimum crew compositon is defined here:
EU OPS (965) Subpart N
Ops 1.940 Composition of flight crew
(b) Minimum flight crew for operations under IFR or at night. For operations under IFR or at night, an operator shall ensure that:
for all turbo-propeller aeroplanes with a maximum approved passenger seating configuration of more than nine and for all turbo-jet aeroplanes, the minimum flight crew is two pilots; or
aeroplanes other than those covered by subparagraph (b)1 above are operated by a single pilot provided that the requirements of Appendix 2 to OPS 1.940 are satisfied. If the requirements of Appendix 2 are not satisfied, the minimum flight crew is two pilots.
And then the much longer Appendix 2 stating:
(a) Aeroplanes referred to in OPS 1.940(b)2 may be operated by a single pilot under IFR or at night when the following requirements are satisfied:
the operator shall include in the Operations Manual a pilot's conversion and recurrent training programme which includes the additional requirements for a single pilot operation;
in particular, the cockpit procedures must include:
(i) engine management and emergency handling;
(ii) use of normal, abnormal and emergency checklist;
(iii) ATC communication;
(iv) departure and approach procedures;
(v) autopilot management; and
(vi) use of simplified in-flight documentation;
the recurrent checks required by OPS 1.965 shall be performed in the single-pilot role on the type or class of aeroplane in an environment representative of the operation;
the pilot shall have a minimum of 50 hours flight time on the specific type or class of aeroplane under IFR of which 10 hours is as commander; and
the minimum required recent experience for a pilot engaged in a single-pilot operation under IFR or at night shall be 5 IFR flights, including three instrument approaches, carried out during the preceding 90 days on the type or class of aeroplane in the single-pilot role. This requirement may be replaced by an IFR instrument approach check on the type or class of aeroplane
(text is copy-pasted since getting a working link to a consolidated version of EU-OPS is a pain)