I wrote in my profile that I like to talk about the music used in anime, but I haven't made it a topic yet. It's time to change that and I'll start with my favorite international, non-japanese openings. All of the songs I picked are either englisch or german songs because I'm a little bit biased and influenced by nostalgia. Sorry! 
I'd also love to know your personal top 3-5, so feel free to share them with me 
The first one I picked is also the most convoluted choice. It's the song "People" by Dax Riders. The song was used in germany as opening song for the show "The Vision of Escaflowne" when it started airing on MTV in 2002.
Dax Riders are a french House and Techno group, which made an englisch song for a german audience used in a japanese fantasy isekai. Nothing fits together, but it's still a great song.
My second pick is the german opening for the show "Nadine - Stern der Seine" also known as "La Seine no Hoshi". The anime started airing in germany in 1998, but it's actually from 1975.
It's one of the releases that found its way onto our TVs around the same time as Lady Oscar and also revolves around the french revolution.
Sadly I didn't find anything about the artist behind the song, but it's one that feels very nostalgic and warm to me.
The next one is a bit of a grey area because it's one of the shows that changed a lot with the localization. My pick is the american opening of "Saber Rider & the Star Sheriffs". The 1988 show is loosely based on the anime "Sei Jushi Bismarck" and got its own music by composer Dale Schacker.
Even if I also like the japanese song "Mystery CALL ME" by MIO a lot, it doesn't compare to the american rock anthem.
Your destiny will lead you
To where ever people need you
Let's get to another german song.. and this is a big one. I'm talking about "Sag das Zauberwort" by Tina Hierstetter. This song was one of the most 90s decisions of all time. While japan had a beautiful opening for Sailor Moon with Moonlight Densetsu and a lot of countries used it as inspiration, germany said no! It's the middle of the 90s. We need Eurodance!! AND. I. LOVE. IT.
@To
Agreed!
@pkemner It's just so fitting for the time. Especially with european music trends from this period. I'm so down for it.