How many times Vegeta has surpassed Goku in power?
Vegeta has surpassed Goku on a few occasions! Only for a short duration though. Here is a list of all the times Vegeta surpassed Goku.Android Saga(When Vegeta First turns SSJ): It was mentioned by Picollo when Vegeta turned SSJ that he was notably stronger than Goku. This was the same time Goku was infected with the heart virus. Cell Games(Post HTC): Once Vegeta and Future Trunks came out of the HTC just before Goku went in with Gohan, Vegeta was obviously stronger than Goku then.Battle of Gods(vs Beerus): This is notably the highest margin by which Vegeta has surpassed Goku. Base Vegeta was definitely as stronger or weaker than Base Goku at this time. The SSJ2 transformation is a 100 times multiplier while the SSJ3 is a 400 times multiplier. Vegeta surpassing the same with his rage boost, made him a lot stronger than SSJ3 Goku.6 Months of training with Whis: We do not know this to a certainty, however, it was stated by Goku once he went to Beerus's world to train with Whis that Vegeta might be as strong or possibly even stronger than him. Rematch against Goku Black(Note: Kaioken is not considered here because it is a special technique): While Goku was mastering the mafuba, Vegeta trained in the HTC and surpassed Goku. Vegeta overwhelmed Black until he converted his ki blade to a scythe.(Black was slower, yet his power had surpassed Vegeta's again). Also, note that this might not be very accurate because we see Goku pushing back a holy wrath from  Merged Zamasu and fighting him on his own while Future Trunks(SSJ Rage)+SSJB Vegeta together struggled to push back a beam attack from Merged Zamasu. My only explanation for the same is that Goku got a Zenkai Boost which made him as strong as Vegeta was by the end of this arc.