[Big up-front disclaimer - this is amateurish, random & composed of wild speculation. Take this seriously at your own risk. That said, I'll try to clarify my reasoning where I can, so you can form your own conclusions.]
A Game of Thrones (George RR Martin) isn't exactly the gutsiest call as a "collectible". As the first volume of The Song of Ice and Fire, this is the volume that propelled Martin from a midlist SF author to a best-selling sensation. Collectible (signed / first edition / etc) printings of A Game of Thrones are already expensive.
Job done, right?
Still, after a peak around 2000, the value of these books has flattened.
After the jump, three good reasons why it'll go up again.
1) The HBO series. Not sure if this is a long-term or a short-term spike, it'll depend on the success of the show. Regardless, this will boost awareness of the series and extend it to a larger audience.
2) Dance of Dragons (Book 5) will come out. Someday. This won't impact the value of signed copies (as he'll invariably be on tour), but it will add some briskness to the trading of earlier first editions.
3) Martin fans are lunatics. I'm not kidding. Even with the beautiful collectible editions printing & reprinting, there will always be a demand for the rare, early editions, if only for bragging rights. There's no sign of fading, either. Martin is a major influence on the current crop of popular fantasy writers.
There are several variants of the "first edition". The rarest and most valuable is the UK proof. There were only a few copies (nobody thought it was going to be a hit at this point) and they went out before the US book went on the market.
The other to watch out for is the US first edition (Bantam, 1996, silver jacket). The US was meant to be released after the UK, but US first editions were handed out early at trade shows like ABA. So the release order was something like: UK proof, US proof, US first, UK first. Fun times. The UK first still sells for a bit more (scarcity), but the US first is arguably more significant.
The "wild card" is the Meisha Merlin limited edition, released in June 2000. 500 copies (448 numbered, 52 lettered) and sold out immediately. This skimmed the top end off the market - buyers looking for high-end, collectible versions gravitated towards this edition as the latest shiny object. The fan base, however, has continued to grow, and, as time has passed, this edition no longer sparkles quite as brightly in comparison to the true first(s).
Weird fact: You can get Martin's earlier work for a song. After a quick, sharp leap in value, everyone has largely ignored the decades of (award-winning) science fiction and horror work he wrote before A Game of Thrones. Apparently the halo effect of his popularity doesn't extend across genre lines.
Conclusion: Already expensive, but more likely to increase than to decline in value.