Ash's most powerful Pokemon is either going to be Pikachu or Charizard. Both have faced some very powerful foes and have taken down their fair share of legendary Pokemon. The two are Ash's go-to Pokemon when it comes to important tournament showdowns also.
Pikachu: The first showing of Pikachu's power is when it proves itself able to defeat Pokemon that are of the Ground type. While it did get some help from the sprinkler system, it was still able to overcome Brock's Onix. It would later prove itself able to overcome Roark's Onix in the Sinnoh episodes. It was able to defeat a Raichu by taking advantage of the lack of moves it learned by skipping to a Raichu right away. Probably the most significant of its early victories however was against Drake, the champion of the Orange Islands. His Dragonite was an incredibly fearsome Pokemon, able to take down Ash's Squirtle, Tauros, and even his Charizard. However, Dragonite eventually fell to Ash's Pikachu. Pikachu also proved to be incredibly powerful in the Battle Frontier episodes, beating Anabel's Alakazam (which had defeated Corphish and Tauros) as well as defeating Brandon's Regice. Pikachu was later able to defeat another legendary Pokemon, drawing Tobias's Latios to a standstill. Pikachu was able able to defeat Trip's Serperior. Pikachu has proven time and again to be able to launch incredibly powerful attacks, really only losing due to its glass cannon nature.
Charizard: As a Charmander it was able to defeat a very dangerous Primeape (this Primeape would be captured by Ash). Charmander would prove able to defeat Pokemon it had a type disadvantage against, defeating a Golem. It was also able to beat Koga with relative ease. When it evolved into Charizard, it would face its first real challenge against Blaine's Magmar, which it eventually defeated. While it lost against its clone, Charizard was a much better match against the clone then the other starter Pokemon. Charizard was also able to stay in battle for a time against an Entei. It also won Ash's final Johto badge by defeating Claire's Dragonair. Charizard proved invaluable during the Johto Conference, not only beating Gary's Blastoise but also beating Harrison's Blaziken (but not before going down first, losing the match. However, it was able to deal enough damage to Blaziken to prevent it from being used in Harrison's next match, causing Harrison to lose.) Charizard was able to defeat an Articuno during the Battle Frontier episodes.
Special mention should also be made for Ash's Sceptile. While not as powerful as Pikachu or Charizard, it was able to accomplish the task of beating Tobias's Darkrai, a feat which had until then not been managed (Darkrai was able to single-handedly sweep the Sinnoh Gym Leaders). While Darkrai was weakened from Ash's previous Pokemon, this damage was negligble as Darkrai managed to heal off most of the damage using Dream Eater.
Thanks to bulbapedia for filling in for me the information of the Sinnoh and Unova sagas, which I have not seen.