LogFAQs > #986448068

A Cruel Angel's Thesis (Neon Genesis Evangelion)
Tank! (Cowboy Bebop)
Go! (Naruto)
Cha-La Head-Cha-La (Dragon Ball Z)

I think this is pretty difficult because while I like these, they are not personally in my top 4. I think ACAT and Tank are locks no matter what.

List of honorable mentions (Listed in order of anime release. This list is no exhaustive)

Moonlight Densetsu (Sailor Moon)
Pokemon Theme (Pokemon DUB)
Inner Universe (Ghost in the Shell Stand Alone Complex)
Haruka Kanata (Naruto)
Blue Bird (Naruto: Shippuden)
Lilium (Elfen Lied)
Red Fraction (Black Lagoon)
Colors (Code Geass)
Motteke! Sailor Fuku (Lucky Star)
Pre-Parade (Toradora!)
Again (Fullmetal Alchemist Brotherhood)
Lion (Macross Frontier)
Platinum Disco (Nisemonogatari)
Crossing Field (Sword Art Online)
Out of Control (Psycho Pass)
Guren no Yumiya (Attack on Titan)
The Hero!! (One Punch Man)

Picks were chosen more so in how I perceived their (lasting) impact on the anime community. So some OPs I think are very good, like Re:Re (Erased), Bravely You (Charlotte), and Daia no Hana (Black Cat) don't make the cut. As are OPs that had mass relevance but have fall out into "obscurity" like Bon ApptitS (Blend-S) and Onegai Muscle (How Heavy are the Dumbbells you lift?)... so ones that were short lived memes.

Finally, some OPs are strong contenders, but the shows ED(s) are just way more iconic, this includes Haruhi, JoJo, Clannad, K-on!, and Bakemonogatari