For a rear light, I use a Cateye model, a TL-100 (a special model for the UK market, not listed on their site). It is powered by 2 AA batteries with the light output being provided by ultra-bright light emitting diodes. I find it very bright and gives good visibility and excellent battery life, 2 factors which lead me to overlook it's slightly poor build quality. I mount it on the rear mudguard, as it's just about the only place on the bike that doesn't get obscured by stuff on the carrier - the light is actually designed to be fitted to the seat post, but I find that idea dangerous, as clothing hanging over the rear of the saddle like jackets and suchlike could obscure it. The batteries last for months due to the low power drain of the diodes.
Mounting the light on the mudguard has two disadvantages; I had to drill the case of the lamp for the mounting bolt, and the weight causes eventual breakage of the mudguards. I have had a couple of these lamps in four years, and on both, the on/off switches have failed due to water ingress. I'm actually looking at making a regulator and flasher unit for this lamp, powered from the front-light battery, thus bypassing the switch. I realise flashing rear lights are illegal when mounted on a bicycle, but sod the law - I'd rather be seen and illegal than legal and dead.