If you shoot handheld, you want a lens with built-in image stabilization (unless you use a camera that has sensor-shift stabilization, which works with all lenses; Pentax and Sony DSLRs offer sensor-shift stabilization).
Canon’s IS, Nikon’s VR, Sigma’s OS, Tamron’s VC and Tokina’s VCM lenses have built-in optical image stabilizers, which move a special group of lens elements to counter camera shake. In the mirrorless world, Pentax and Samsung OIS lenses provide optical stabilization (Olympus mirrorless cameras have sensor-shift stabilization). These systems really work, allowing you to get sharp handheld images at two to four shutter speeds slower than would be possible otherwise.
In Canon’s original IS system, a vibration gyro detects the angular velocity component of lens motion caused by camera shake and transmits this data to a microcomputer, which converts it to a stabilizer optical system drive signal, which is transmitted to the magnet-and-coil stabilizer optical system drive circuit, and the compensation is applied by shifting the compensating element group appropriately. Stabilization Mode 2 lets you pan the camera to track action subjects while still having compensation for vertical camera shake. Tamron’s VC system uses a tri-axial configuration with three pairs of driving coils and low-friction ball bearings around the lens’ shake-compensating group to, in effect, provide a free-floating shake compensation for diagonal as well as up-down and side-to-side shake. Olympus’ higher-end mirrorless cameras provide 5-axis image stabilizing, compensating for horizontal shift, vertical shift, yawing, pitching and rolling motions. Generally, new stabilization systems are more effective than earlier ones, but even the early ones are much better than no stabilization.
Conventional spherical lens elements focus light rays traveling through the center farther behind the lens than rays traveling through the edges. This is called spherical aberration, and it’s most evident in shorter focal lengths and at wider apertures (especially with fast lenses). Aspherical elements can minimize spherical aberration, as well as distortion, so are often found in wide-angle and fast lenses, as well as zooms.