Power side-channel attacks exploit variations in power consumption to extract secrets from a device, e.g., cryptographic keys. Prior attacks typically required physical access to the target device and specialized equipment such as probes and a high-resolution oscilloscope.In this paper, we present PLATYPUS attacks, which are novel software-based power side-channel attacks on Intel server, desktop, and laptop CPUs. We exploit unprivileged access to the Intel Running Average Power Limit (RAPL) interface that exposes values directly correlated with power consumption, forming a low-resolution side channel.We show that with sufficient statistical evaluation, we can observe variations in power consumption, which distinguish different instructions and different Hamming weights of operands and memory loads. This enables us to not only monitor the control flow of applications but also to infer data and extract cryptographic keys. We demonstrate how an unprivileged attacker can leak AES-NI keys from Intel SGX and the Linux kernel, break kernel address-space layout randomization (KASLR), infer secret instruction streams, and establish a timing-independent covert channel. We also present a privileged attack on mbed TLS, utilizing precise execution control to recover RSA keys from an SGX enclave. We discuss countermeasures and show that mitigating these attacks in a privileged context is not trivial.