Hmmm.....for me I would say Sword Summit from the second season of Sengoku Basara and Wild Wild Rock from Saiyuki Reload. Those are freaking catchy! XD
*Unranked*
Zankoku na Tenshi no Thesis (Neon Genesis Evangelion)
Uninstall (Bokurano)
Guren no Yumiya (Shingeki no Kyojin)
Crossing Field (Sword Art Online)
To The Beginning (Fate/Zero)
Toki wo Kizamu Uta (Clannad After Story)
Aoi Shiori (AnoHana)
Connect (Mahou Shoujo Madoka Magica)
Niji no Kakera (Isshuukan Friends.)
Visually my favorite anime opening is Shakugan no Shana II OP Blaze, Fullmetal Alchemist Brotherhood OP Again, and Baccano Op? There might've been more..
Music..there are too many good ones. Right now Captain Planet OP, Haikyuu op, Tokyo Ghoul op, I like the song for Brotherhood too..a couple of Katekyo Hitman Reborn theme somgs too..so many themes.