lol I've read a lot that says Amuro Ray is the best, but I've never seen the original Gundam. Is he 1337hax0r?
Ok, basically, by the end of the first series, the Gundam has been mass-produced by the Earth Federation, and the mass-produced Gundams (GMs) are basically the same as the Gundam itself except with less armour etc. Meanwhile, Zeon (the enemies) have developed mass-produced mobile suits called Gelgoogs which are actually more powerful than the Gundam (higher specs, more weapons, etc.), whilst also having an arsenal of overpowered Mobile Armours+special ace suits (including a giant tank-like Mobile Armour that is more or less impervious to any ranged weaposn). Basically, imagine SEED if Kira was stuck in the Strike Gundam for the whole series, and that's roughly where Amuro's technology is at compared to the enemy's Forbidden Gundam+Raider Gundam+Calamity Gundam, fleets of GuAIZs, etc.
In the final battles of the series, Amuro isn't just winning; he is absolutely owning everything Zeon throws at him, including custom-made super-powered mobile suits, and the Gundam itself (which is still more or less state-of-the-art) is actually struggling to keep up with his piloting skill. I believe there's one oft-quoted feat where Amuro destroys 14 higher-end mobile suits in less than a minute (using a beam rifle and a beam saber). In the series' final battle, Amuro defeats Char Aznable (who is well known enough for people to basically **** their pants when he comes along) whilst piloting a far-inferior mobile suit.
It doesn't stop there though. Unlike most Gundam protagonists, Amuro basically lives as a soldier for most of his life. Before we move on though, consider that by the end of the first series he has acquired the nickname "White Devil", purely on his piloting skills given that the Gundam's performance isn't actually better than most of its enemies about halfway through the original series.
Anyway, by the time of Amuro's last appearance (Char's Counterattack), he's a well known test pilot and is so pro that the Earth Federation government is too scared to lend him any mobile suits which could potentially utilise the full extent of his Newtype powers. The opening of the Char's Counterattack movie sees Amuro using a glorified grunt suit to more or less defeat Char (in the most powerful mobile suit in the entire film) plus another ace guy in a Newtype-enabled ace suit with funnels. Then Amuro gets his Nu Gundam and (accompanied by like a squad of grunts and a battleship) singlehandedly takes down Char's entire fleet, which is comprised entirely of the aforementioned ace-style suits (which have funnels), a monster of a mobile armour (with funnels, beam field, BFG, etc.), battleships and even Char himself. Finally, Char decides to push a giant asteroid base onto the Earth to effectively nuke all life on it...except Amuro literally goes up to the asteroid and with the help of his Newtype powers actually manages to PUSH THE FREAKING ASTEROID BACK INTO SPACE AFTER IT HAS ENTERED THE ATMOSPHERE.
Also, note that like 90% of his opponents are Newtypes.
Not only are Amuro's feats ridiculous, but as a pilot he displays ingenuity which is unmatched once compared to basically any Gundam pilot apart from Garrod Ran from Gundam X (and Garrod is basically known entirely for his intelligence and resourcefulness). Along with conventional fighting (ie. shooting the enemy), Amuro utilises basically every trick in the book to great effect in fighting; he drops weapons in front of himself to throw off the enemy's attention, he uses dummy balloons to distract the enemy, etc. all the time whilst maintaining an offensive, keeping him a level above pretty much any other ace ever (and you thought Shinn was smart in his defeat of the Freedom Gundam...).
This video basically embodies Amuro's raw piloting talent:
http://www.youtube.com/watch?v=IpA-1sozp_ENote how unlike Celestial Being and the Strike Freedom, Amuro doesn't have the weapons available for him to do anything apart from basically take out his enemies one by one (the Universal Century funnels are mind controlled, so you can't really spam them).