This is what I do for a living, my company is the largest retailer and distributor of classic video games in North America (and most likely the world). Over the years we've built up a database with hundreds of millions of price points and sales transactions for tens of thousands of games. The overall trends haven't changed much, and with most games it's fairly easy to tell if the value is going to increase or decrease.
First, if you are talking about a new game - if you open it then it is highly unlikely the game will become worth more than you paid for it any time soon. If you don't open it and it is a limited edition or collector's edition, and actually contains figures, books, artwork, etc, it may increase in value. If it ends up being a popular game it can skyrocket in value, especially if no one expected it to be a huge success when it first came out. We bought several copies of the original Mass Effect Limited Edition in 2007, never opened them, kept the receipts, paid 69.95 for each and sold them all for over 1k each last year. During its peak unopened copies of the original World of Warcraft were going for several thousand dollars. But those are the exceptions. RPGs tend to do far better than other genres, most other games will lose value even if unopened.
Now if you are talking about older games, its a completely different story. For the last 8 years prices for classic video games have been going up at a steady, rapid rate. There are a few main factors. 1) - People get older, get better jobs, have money, and want to either replay the games they loved as a kid, get the games they couldn't afford when they were young, or show the games to their own children. 2) - International buyers are buying a HUGE number of classic video games - many of them were never released in their country and they only way they can legal play the game is to import it from the US. 3) - These games aren't made anymore. The supply is only decreasing. A decreasing supply combined with a rapidly increasing demand means price increases.
As long as people continue to enjoy collecting games, and as long as they continue to enjoy playing classic games on the original systems, prices are likely to increase, although more slowly than in the past. Virtual Console, PSN, and other re-releases usually result in a small increase in demand for the original games (unless they were already way too expensive). Roms have been around for far longer than we've been doing this and the demand for the originals, and the prices, are still increasing. But keep in mind that unless you are talking about unopened games, then the prices are increasing relative to their value a few years ago. A good, new NES game for bought for $60 in 1988 may only be worth $20 today. But in 2010 you could have bought it for $6. In 2008, $3.
If you have a bunch of old video games and need some cash, I'd sell them. Don't count on them to skyrocket in value. But if you don't need the cash and if you still enjoy playing them, it's fine to hold on. They should continue to increase in value. If they are new games - sell them as quick as you can! But not to GameStop. Sell them on Ebay or Craigslist. Places like GameStop will rip you off and give you half what you could have gotten selling it yourself.