(My definition of open world here is different from the one used in the other topic; in particular, I am looking at the game's structure (lack of linearity and artificial barriers), rather than scale.)

Basically, I am looking for an open world (in the sense that there are few or no arbitrary barriers preventing you from going almost anywhere at the start) RPG like the original Dragon Quest. Here are some things I am looking for:
* Game must not have enemy scaling; enemies should get more difficult the further you go from the starting point.
* It should not be realistically possible to survive more dangerous areas when at low levels. In particular, games where you can avoid every combat at low levels, or where a sufficiently skilled player can (without resorting to things like RNG manipulation) simply avoid getting hit (like most action games), are not what I am looking for.
* In general, the gameplay dynamic I am looking for is where you start out weak, but slowly build up power, and as you get more powerful, you can explore more dangerous areas of the world, allowing you to become even more powerful until you are strong enough to beat the game.

Many classics would fit that description: Fallout 1&2, Baldur's Gate for example come into my mind. Also Morrowind fits the description. Gothic 1&2 also were pretty open and didn't had level scaling.

Pillars of Eternity on Path of the Damned difficulty fits this quite well as I recently found out. Fallout 1 & 2, Gothic 1 & 2, and Baldur's Gate series as was already mentioned. Tales of Vesperia on harder difficulty settings fits. Star Ocean: The Second Story for sure.

I'm gonna take a wild guess that I don't need to mention Final Fantasy and Phantasy Star as i'm sure you've already played those if you've played Dragon Quest like I have.

Uh, trying to think of others but my mind is blank. :P

Actually, Final Fantasy and Phantasy Star aren't what I am looking for, nor are the later games in said series. The problem is that those games, while some of them may open up, don't actually do so until later on. On the other hand, Dragon Quest 1 theoretically lets you go almost anywhere from the start of the game. Not familiar enough with the rest, but one problem with Morrowind is that a skilled player can avoid combat entirely, particularly if she is playing a fast character. In Dragon Quest, avoiding combat entirely is not going to happen unless:
1. The player uses a skill or item which only works on lower level enemies, or
2. The player manipulates the RNG to an absurd degree, which has only been possible without tool-assistance recently and is not something a casual player will be able to do.

(Also, Morrowind's combat density is too low for my tastes (too little time spent in combat compared to exploration), and the game's growth system is rather ugly, requiring not-so-fun gameplay if you want to get good stat growth at level up.)

Because somebody mentioned it, Star Ocean 2 isn't open enough for me, since you can't reach any areas from the second half of the game before clearing the first half; also, it's a bit too cutscene heavy for what I am looking for. There's also the problem with permanent missables, including one particularly bad one that you can be screwed out of just because you were unlucky at the start of the game (and can't check right away because, of course, the game starts with a cutscene that you need to re-watch every time). (In case anyone is wondering, I have played that game, and I prefer playing as Rena rather than as Claude.)

Ah, I think I understand better now.

Hmmm, the Ultima series kind of does the things you mention and certainly allows you to go anywhere from the start, but I wouldn't say those games are quite as difficult unless you go far off unprepared. Though Ultima was one of the inspirations behind Dragon Quest 1. Trying to think of others, it's been such a long time lol.