I wonder which the English language purists find more annoying, the wholesale import of words from geek and computer user slang (such as "w00t", "pwned", and similar words), or the current craze in importing Japanese words? I'd suspect offhand that the geek words are actually more annoying, because they're often deliberately misspelled versions of English words.
The Japanese word that's transliterated "Yatta!" looks to fill a similar linguistic niche to the geek "w00t". It appears to be translated as, varyingly, "I did it!" "We did it!" "All right!" -- in other words, a fairly all-purpose exclamation of success and accomplishment.
If all of that is too modern or foreign, however, why not revive the noble "Huzzah!"