The legendary side-scrolling action-RPG compendium.

Oh man I could list like 100083743783 billion if I didn't have two babbies sitting on me.

Off the top of my head, most Dragon Slayer games qualify. Xanadu, Romancia, Legacy of the Wizard, Sorcerian, and both Legend of Xanadu titles. Multiple platforms.
The XZR (Exile) trilogy.
Gensou Tairiku Auleria (PCE CD).
Jikuu Yuten: Debias (Famicom)

Many, many more. This can be a tricky list given how rudimentary some of the "leveling" systems are in these games. Hard to tell what's a true ARPG and what's "just" a Metroidvania.

I just finished one, come to think of it. Cadash counts, even if it's pretty simple structurally. Arcade, TG-16, and Genesis versions.

If leveling is involved, then... I guess all the Igavanias count? Figure so, even if they're also under the Metroidvania rubric.

Maybe Odin Sphere, it just squeezes in under the ten-year bar.

Games like Wonder Boy: The Dragon's Trap/Curse) get close, but no leveling, so it's more Metroidvania. But they are awfully close in construction barring that fact.

Oh, I just realized, does Battle of Olympus even have a leveling system? I'm not sure it does. It does have a monetary system like the Monster World games, so I suspect if Olympus counts, the MW games need to as well.

Well, you can jump, anyway.  I think there might be a few cliff faces you have to climb, but the platforming is extremely rudimentary.  I'd probably leave it off, in retrospect.  It's more side-scrolling brawler-RPG than what we're looking for.

I'd still consider leaving Olympus in, personally. It just feels like it belongs, if that makes any sense. In a lot of ways, games with equipment upgrades where you have to purchase them is practically like leveling, it's just abstracted to that single money stat instead of an experience and money pool.

Now that I think about it, Bio Senshi Dan may not have an explicit leveling system either.  I know your health pool increases, but that may simply be based on defeating the main boss of an area or progressing to the next stage. 

Just thought of one: Rambo on NES. For reals.

Strider gets close.  You gain levels, but it's not from an experience meter, but on killing certain bosses, gaining certain items, or various plot points.  To some degree Bionic Commando has some ARPG stylings as well, with a rudimentary EXP system with the life gauge.