Recent advances in solid-state technologies have enabled the development of light-emitting diodes (LEDs) with favorable features such as long life expectancy, low-power consumption, and reduced heat dissipation. Visible-light communication (VLC) is a short-range wireless access technology that deploys LEDs as wireless transmitters in addition to their primary task of illumination. The major limitation for the design of high-speed VLC systems is the electrical (modulation) bandwidth of the LED. In this study, we investigate the electrical characteristics of a number of off-the-shelf LEDs. Specifically, we determine their frequency responses and match them to their small-signal models. The electrical bandwidths of measured LEDs vary from 250 kHz to 20 MHz and depend on the emitted color and internal circuitry. As a verification of our measurements, we use the sample LEDs as a transmitter in a VLC system setup and determine the supported data rates. The equivalent circuit model is utilized to compare with the measured modulation characteristic of the LED. Furthermore, the bias current effect on the modulation bandwidth is presented.