Yes! We have several 100% TypeScript applications and we've found TSLint to be invaluable for maintaining code quality - http://palantir.github.io/tslint/

You can ban the `any` type along with lots of other rules. You can also write your own custom rules, or implimnet rulesets by 3rd parties like Microsoft: https://github.com/Microsoft/tslint-microsoft-contrib and ESLint: https://github.com/buzinas/tslint-eslint-rules