Has there ever been a successful satellite launch done by amateurs? I mean both building the satellite and a rocket to carry it.
2$\begingroup$ No, amateur satellites are secondary payloads of commercial launches. It is not possible to reach the orbital velocity required without large research and investments. Once Russians were also firing converted missiles from submarines, offering paying launches. Solar sail Cosmos-1 was lost this way, when it failed to separate from the missile. $\endgroup$– minsAug 21, 2015 at 7:02
1$\begingroup$ Top Gear tries to put a car into orbit but the car didn't detach correctly from the space shuttle $\endgroup$– clemtoyAug 21, 2015 at 8:53
2$\begingroup$ Oh yes, Top Gear, bleeding edge rocket developers. $\endgroup$– Russell BorogoveAug 21, 2015 at 14:17
No, in fact, it's very difficult to even reach the threshold of space (50 miles or 100 km) by amateurs, they've never even gone close to the required velocity to achieve orbit. See the Amateur Rocket Wikipedia page. Basically, it's really really hard to build a rocket, taking a company like SpaceX years with many engineers to achieve success, and it just seems outside the range of amateurs at this time.
As was mentioned in comments, Amateur satellites are always secondary payloads on larger missions. There have been a number of these missions launched.
$\begingroup$ @KrzysztofMajewski That's not stopping some from trying (to reach the threshold). See Copenhagen Suborbitals in one of the answers to my question here. $\endgroup$– called2voyage ♦Aug 21, 2015 at 15:23
1$\begingroup$ They'll have to change their name if they want to launch a satellite that lasts more than a few minutes. $\endgroup$ Aug 21, 2015 at 16:50
1$\begingroup$ @RussellBorogove Notice in my parenthetical statement I indicate that they are trying to reach the threshold, not orbit. I was answering the first part of Pearson's answer where he says "No, in fact, it's very difficult to even reach the threshold of space [...] by amateurs". $\endgroup$– called2voyage ♦Aug 26, 2015 at 14:43
Actually they were not always done as secondary payload, in the early day of CubeSat (check out CalPoly CP CubeSats, CalPoly P-POD). Those were launched on modified ICBM specifically for the CubeSats (not in US). The practice was picked up and modified by NASA to put them as secondary payload mostly for educational purpose. But back to your question, it is very difficult for amateur to get to space, hence most academic focuses mostly on building CubeSats or instruments.