I must admit I don't have much love for English Openings, most of them were your average cartoon songs and some even way bellow average (second, tenth and all dubbed Kalos Openings). However, there are three which stand for me. The first is classic, though thinking about it now, it was just that, classic I've heard in fall 2000 every Saturday and Sunday morning (until they replaced it with Czech version, which wasn't all that good IMO, but hearing some other language versions of the song, we still got it quite well). The third was IMO the best dub opening and the only one who felt like I am watching Anime, not American cartoon. And then there's eleventh, which was really great song and, correct me if I am wrong, first dub opening sung by woman. After first two PUSA (now TPCI) openings, which were nothing but disappointment (especially the tenth song, which is IMO the worst Pokémon opening), this was really great refreshment.
For Japanese songs, this will be harder, since I love all of them (though I could live without all those Mezase remixes), but I'll probably go with first Mezase, OK!, Advanced Adventure and Getta Ban Ban as my most favourite, but don't want me to choose the best from them, as I wouldn't be able to do so.