Security architectures providing Trusted Execution Environments (TEEs) have been an appealing research subject for a wide range of computer systems, from low-end embedded devices to powerful cloud servers. The goal of these architectures is to protect sensitive services in isolated execution contexts, called enclaves. Unfortunately, existing TEE solutions suffer from significant design shortcomings. First, they follow a one-size-fits-all approach offering only a single enclave type, however, different services need flexible enclaves that can adjust to their demands. Second, they cannot efficiently support emerging applications (e.g., Machine Learning as a Service), which require secure channels to peripherals (e.g., accelerators), or the computational power of multiple cores. Third, their protection against cache side-channel attacks is either an afterthought or impractical, i.e., no fine-grained mapping between cache resources and individual enclaves is provided. In this work, we propose CURE, the first security architecture, which tackles these design challenges by providing different types of enclaves: (i) sub-space enclaves provide vertical isolation at all execution privilege levels, (ii) user-space enclaves provide isolated execution to unprivileged applications, and (iii) self-contained enclaves allow isolated execution environments that span multiple privilege levels. Moreover, CURE enables the exclusive assignment of system resources, e.g., peripherals, CPU cores, or cache resources to single enclaves. CURE requires minimal hardware changes while significantly improving the state of the art of hardware-assisted security architectures. We implemented CURE on a RISC-V-based SoC and thoroughly evaluated our prototype in terms of hardware and performance overhead. CURE imposes a geometric mean performance overhead of 15.33% on standard benchmarks.