Games that involve platform gameplay with non-linear, exploratory design, are often called Metroid-style games. Nintendo's 1986 epic was an amazing game that popularized this type of design. I'm a big fan of these types of games from Metroid, to the Monster World series, to later Castlevanias to Cave Story.
http://www.the-nextlevel.com/hosted/...roid%20nes.bmp
Metroid can't take all the credit though as there were similar games before it. This thread is about those games.
Non-linear platform/adventures date back at least as far as 1983. Like I mentioned in the Synapse Software thread, Pharaoh's Curse was one of the these. It was released for Atari 8-bit, Vic 20, and Commodore 64.
http://www.the-nextlevel.com/hosted/...haraohsc64.gif
Like Metroid, Pharaoh's Curse consists of interconnecting rooms that can be explored in whatever direction you chose. It involves finding various items as well. It was also one of the earliest games with a password feature; once you collected all the treasure, it gave you a code for a harder mode. I recommend checking it out as it has aged quite nicely.
I think Epyx's 1984 computer game Impossible Mission deserves a mention too. It's a bit less Metroid-like than Pharaoh's Curse in style but it does have the similarity to the Metroid series in that when you beat it, it lists the number of items you found, and your time so you can try for a better run through.
http://perso.numericable.fr/~ckckck/...le_Mission.gif
Also from 1984, there's Matthew Smith's Spectrum game Jet Set Willy. JSW expanded on its predecessor, Manic Miner, by having a non-linear world to explore with many treasures to collect.
http://www.the-nextlevel.com/hosted/...et%20willy.gif
The games listed above are missing a key element of Metroid-style games though, and that's the ability to shoot enemies. Ultimate's 1984 Spectrum game Underwurlde(part of the Sabre Wulf series) does have that element. The rope you can use to hang from also reminds of grappling hook in later platform/adventures including Super Metroid.
http://www.the-nextlevel.com/hosted/...nderwurlde.gif
Loriciels released Infernal Runner in 1985 for the C64 and later on the CPC. I never beat the game as a kid but it stood out for me because of the various gruesome ways you could die. Blood spatter was rare in games back then. Like other games mentioned, it consisted of interconnecting rooms and finding items.
http://www.the-nextlevel.com/hosted/...l%20runner.gif
The CPC version(ported by Out of this World creator Eric Chahi) is free to download. http://www.loriciel.org/fiche.php?id=32
1985's Nodes of Yesod and its sequel Arc of Yesod, by Odin Computer Graphics for the Spectrum(and ported to other computers), remind me a lot of Metroid.
http://www.the-nextlevel.com/hosted/...ater/nodes.gif
So far we have come quite close to Metroid's design. One notable difference is that the games mentioned above are focused on collecting items but not really on ones that upgrade your character/suit. Palace Software's The Sacred Armour of the Antiriad(later released by Epyx in North America as Rad Warrior) does do this.
http://www.the-nextlevel.com/hosted/...r/antiriad.png
Out of the hundreds of pirated C64 games I had as a kid, I'm surprised and a bit disappointed this wasn't one of them. My first exposure to it was the crappy CGA DOS port. The game was also on Spectrum and CPC. A freeware PC remake was made in 2003 although it's pretty ugly.
Antiriad has non-linear platform design, lets you attack enemies, and has you upgrade your abilities which lets you access new places. There aren't as many enemies, and the game is very European in appearance, but structurally, it's almost Metroid before Metroid. Cool stuff.
I highly doubt Nintendo copied the game though. If the June 1986 release date I found is correct, Antiriad came out only a couple months before Metroid's Japanese debut.
The original Spectrum game in Codemasters' Dizzy series also dates from June 1986. It's certainly not as Metroid resembling as Antiriad, and doesn't have much of an action element, but it's still a non-linear platform/adventure.
I'm probably missing some games so please add them or anything else you feel is relevant.

