Emitting electromagnetic radiation (EM) is not possible for an electron that is at rest, traveling at a constant speed, or in the lowest energy state of an atom.
However, electrons that have been accelerated emit electromagnetic energy (EM radiation). This is what causes radiation from radio antennas, synchrotron radiating radiation (where electrons are constantly accelerated in circular paths or “wiggled”, by a series N-S or S-N magnetic field), and Bremsstrahlung. High-speed electrons produce X-radiation when they are quickly slowed/stopped within matter.
Additionally, electrons that orbit the nuclei can be excited to higher energy states by a variety external mechanisms. The transition emits radiation at specific frequencies, infrared, visual, and ultraviolet. Relativistic electrons, i.e. electrons traveling at the speed of light, will produce characteristic bluish Cherenkov radiation when they interact with matter.
In a process known as beta decay, certain radioactive nuclei can also release electrons. This is often called beta radiation but it is actually spontaneous emission of an anti-electron or electron (called a “positron”) from the nucleus radioactive atom.