Four relevant anime examples:
In the older Troma/Fox dub of "My Neighbor Totoro", the younger sister Mei was voiced by Cheryl Chase (voice of Angelica Pickles on "Rugrats").
Chika Sakamoto, who voiced Mei in the Japanese version, voiced Angelica Pickles in the Japanese dub of "Rugrats".
In Viz's 1996 dub of "Galaxy Express 999", the main character Tetsuro Hoshino was voiced by Saffron Henderson (voice of young Goku/Gohan in the Ocean dubs of Dragon Ball/Dragon Ball Z).
Mazako Nozawa voiced Tetsuro in the original Japanese version and also voiced Goku and Gohan in Japanese Dragon Ball/Z.
Wendee Lee voices both the title character from "The Meloncholy of Haruhi Suzumiya" and Konata from "Lucky Star" in the English dubs. Aya Hirano voiced them in Japanese. There are other examples found in these two shows and were intentional by the dubbing company.
Kappei Yamaguchi voiced both boy Ranma of "Ranma 1/2" and Inu Yasha in Japanese. Richard Cox voiced boy Ranma in the later seasons of the English dub version and also voices dub Inu Yasha.