This topic kind of blew up, and it makes me want to expand my answer on it, lol, since my first post didn't really explain anything. So, I'll agree with those who said it should take as long as you need to establish your intro; that there's no true one answer that fits all games, so I'll just go with what I, myself, prefer to see in games (RPG Maker games, specifically) for this.
Say I download your free RPG Maker game to try it out. See if it's any good (read: fun for me to play). My main interest in RPG Maker games is seeing interesting combat design, so if you start out your game with a lengthy intro that doesn't really let me do anything but to walk over to NPCs and read dialogue boxes, I'm going to be turned off.
See, if a game has a good story, but bad combat, I'll not be compelled to finish the game. Your game can be the next Shakespearean masterpiece, but if your combat is bad, I'll not play it. When I play your RPG Maker game, I'm short on time. I don't have a lot of free time to play a bunch of games, so if your intro needs a bunch of time before it gets to the part I want to play, I'll drop it. Keeping story telling concise and to the point is, in my opinion, a key element to writing for games.
On the other hand, if a game has good combat, but bad story, I can live with that. I'm here to play a game, not to read a novel. Well written story is a bonus if it happens to come with a game that already has good combat. The only way to judge whether a game has good combat or not is by playing it, so the earlier I get to play your combat, the better. If it turns out to be bad, I can drop it early on and I'll have little time wasted on a game I wasn't going to finish. If it turns out to be good, I get to the good part early on, and that is a good thing.
I respect developers that show their gameplay early on. It means they are confident in their gameplay and that their game is fun to play. Developers who lock me into endless boxes of dialogue give me the feeling they're hiding their lack of game developing skills behind walls of text, in the hopes I'll find their story interesting enough to overlook poorly thought out gameplay mechanics.
tl;dr: I play RPG Maker games to play them, not to read them. The sooner you give me combat to play, the sooner I'll know if your game is worth keeping playing.
What's my ideal time to first get into combat?
<1 minute. Great if your game is mainly gameplay-driven. I like this.
1-5 minutes. This is pretty much the ideal window of time, giving just enough time to establish an introduction to your game world and story, but still getting me to play fast without waiting a long time.
5-10 minutes. A bit on the long side, but I can live with it if your intro is well made and engaging in some way or another.
10-15 minutes. This is really stretching it. You need to be doing something very right if you can keep me waiting this long without dropping it before my first encounter.
15+ minutes. I'm moving on to another game.