I've had the Lepai 20W stereo amp for a few weeks. I'm using it with the provided power adaptor (110V mains to 12V @ 2A) which is a small, light SMPS unit that plugs into the wall. You also have the option to connect a 12V battery power supply if you want something portable for travelling, camping, picnics, a busking amp, etc. A rechargeable 12 sealed lead acid (SLA) battery (burglar alarm/emergency lighting battery) would be ideal but remember that you can't take SLA batteries on planes or through security checks.
I have it plugged into a pair of small, low quality bookshelf loudspeakers so I can't really comment on the sound quality. The tone controls (bass and treble) make a noticeable difference and I think have a sufficient range for what you'd expect from a small cheap amp, plus there's a bypass switch. The case and controls have solid construction and I think the unit would survive a few knocks and drops - important if you intend to travel with it or use it for busking. I haven't tested it but I expect the 2A power supply is easily enough to get a full 20W out of the amp without distortion or losing bass response, however, that doesn't mean it wouldn't overheat if played at full volume for long periods of time. It's easily serviceable but, for the price, it's probably cheaper and easier to buy a new one if anything goes wrong with it.
Overall, I'd say it's a bargain at the price, robust and flexible, a decent quality... ...and no, I wasn't paid to write this review! I genuinely like it.