Brillouin slow light in optical fibers is a promising technique for the development of all-optical buffers to be used in optical routers. The main drawback of this technique up to now has been its narrow bandwidth, normally restricted to 35 MHz in conventional single-mode optical fibers. In this paper we demonstrate experimentally that Brillouin slow light with an arbitrary large bandwidth can be readily obtained in conventional optical fibers using a simple and inexpensive pump spectral broadening technique. In our experiments, we show the delaying of 2.7 ns pulses over slightly more than one pulse length with only some residual broadening (<25%) of the pulse width. We see no limit to extend this technique to the delaying of GHz-bandwidth signals.