For gelled CP, I cure 4 weeks. For ungelled CP, 5 to 6 weeks (some people prefer to cure ungelled soaps for 8 weeks). For HP, at least 2 weeks but generally will cure for 4 because while you forced the saponification to finish with the heat of cooking, it still greatly benefits from a cure. I hated the first HP I did at 4 days and it was better at 2 weeks but by the time 4 weeks rolled around, I loved it.
The only soap that really needs to have a long cure, 6 months to a year, is castile. I don't like castile because of the ick feeling it gives me because its lather isn't really bubbly, unless you use one of the nylon shower puffs. Also, I'm not one of them, but I know a few people who prefer to cure soaps with 80% or more olive oil for 8 weeks or more. I'm not one of them because castile is the only one I use more than 50% OO lol