What manned airplanes have achieved flight with the least powerful engines (no gliders!), and what was their top speed? Im sure I've heard of an airplane with an 8hp engine capable of exceeding 120 MPH airspeed
In still air, the required power was on the order of 300 W (0.40 hp), though even mild turbulence made this figure rise rapidly.
As far as top speed:
Allen completed the 22.2 mi (35.7 km) crossing in 2 hours and 49 minutes, achieving a top speed of 18 mph (29 km/h) and an average altitude of 5 ft (1.5 m)
Sailplanes employ zero horsepower by conventional reckoning, though an alternative definition can be proposed using the component of the aircraft's weight that acts parallel to the airspeed vector as the thrust-like force. Anyway, the world records for sailplane flight appear to include 2191 km as greatest free distance along a course involving three or fewer turnpoints, and 22657 m as maximum absolute altitude. Source: fai.org/page/igc-records
OK, I thought the original question said "aircraft"; I now see "airplane". Does "airplane" always exclude "glider"? Originally, the "plane" in "airplane" referred to the "planing" action of the wing surface, and had nothing to do with the presence or absence of a motor, though there may be no specific examples of the word historically being used in reference to gliders.
Didn't see the "no gliders!" when I created this answer-- sorry! Some self-launching powered hang gliders and powered paragliders/ paramotors intended for soaring flight must be close contenders for the answer to your question, as some of them have rather weak engines and are barely able to climb in the absence of an updraft despite overall light weight.
Even though at 4 x 13kW its max rated power (70hp) is higher than the other answers, Solar Impulse flew almost 5 thousand miles non-stop during close to 5 days. It did not typically fly anywhere close to its max rated power in order to conserve energy that it would have to spend during the night.
Wikipedia lists the specs as:
Maximum speed: 140 km/h (87 mph)
Cruise speed: 90 km/h (56 mph) 60 km/h (37 mph) at night to save power
Service ceiling: 8,500 m (27,900 ft) with a maximum altitude of 12,000 metres (39,000 ft)
This is of course much higher than the human-powered Gossamer Albatross in Eugene Styer's answer, but the Wright Flyer, "the first powered, heavier-than-air machine to achieve controlled, sustained flight with a pilot aboard", used a
12 horsepower gasoline engine
which is a bit under 9 kW.
The longest of its 4 flights was 260 m, and it was apparently so light that "a heavy gust picked up the Flyer and tumbled it end over end, damaging it beyond any hope of quick repair".
Later versions used more powerful engines.
The lightest remote control airplane I could find is 0.225g (0.01oz).
Wing span 71 mm.
Length 70 mm. (about 3")
I estimate it used a few hundredths of a watt.
That was back in 2008 though, so they've probably done better since then.
The twin engined Columbian Cri cri might be a contender: each of the single cylinder piston engines were about 15hp. Cruising speed is 190km/h. Wikipedia article