Which carbocation is the most stable?

Stability of alkyl carbocations rises with the number of alkyl groups on the cationic carbon (inductive effect and hyperconjugation). The tertiary cation has nine hyperconjugating C-H bonds, so the order is tertiary > secondary > primary > methyl, and $(\mathrm{CH}{}_3){}_3\mathrm{C}{}^{+}$ is the most stable.