I don't think there's any surefire way, as publishers don't often disclose how large of a run they are going to do, nor what the current demand is. With some of Nintendo's more limited releases, they've indicated as such ahead of release (Super Mario All-Stars, Metroid Prime Trilogy, Zelda w/ Gold Remote).
There are a few methodologies you can employ:
1). Who is the publisher and how big are they? If they are a small publisher (like Atlus, or NIS, or XSEED) the run is likely to be small. The more niche the title, the smaller the run.
2). How did the last game in the series do? If it sold poorly and is still being published despite low sales numbers, it's likely the publisher is going to do a small run to avoid over stock and buy backs. Dragon Quest V (DS) fell victim to this.
3). What's the genre of the game? If it's something Japanese, it's probably getting a small run - those types of games don't do well in America these days.
4) .Where is the game available at release? If you can't find it at the big stores like Walmart, Target, and Best Buy, it's probably a limited production.
With all of this, it's worth keeping in mind that just because something has a limited run that it won't get cheaper and still be easy to find down the road. Stuff like Spyborgs had a very limited run, but sold so poorly that it was easy to track down for years after its release (I just got a copy a few months back).
If you do think a game is going to get a limited run, it's important to keep a very close eye on it. Sites like Cheap Ass Gamer do a great job of tracking game prices and you should use them to your benefit. You can definitely get rare games at cheap prices if you are vigilent about tracking them from the point they hit the market.
Hope this helps - I do have some experience with this. Oh, also of merit - check your local Gamestop, especially during Buy 2 Get 1 sales. You'd be surprised how often you can find these rarer games in phenomenal condition way down the line on the cheap. People who buy those types of games tend to keep them in tip top shape, for whatever reason.