When it comes to prolonging the life span of any piece of electronics, it is best to be proactive. The early signs are not malfunctions, but simply represent an environment which is hostile to the life of a video card.
The first sign of future video card problem is a high GPU temperature. There are several different programs that can check the temperature of a GPU, but I prefer Rivatuner. There are some video cards available today which will in fact run at temperatures as high as ninety degrees Celsius and not see immediate corruption or failure. That said, ninety degrees Celsius is extremely hot and it certainly can't be good for the overall lifespan of the video card. Keeping things below seventy degrees Celsius is probably best. This is not a scientific number, as there has been no through testing ever done of how long video cards last under different environmental conditions. It is a number which most video cards can sustain, however, while it is in the ballpark with maximum temperatures one would want to see on a CPU or a motherboard's northbridge.
Another related early sign of future problems is a fan which seems unusually loud, rattles, or seems to waver in speed. A fan which is not working well could result in higher than desired temperatures. It could also fail, which can certainly cause problems.
General instability is perhaps the most serious sign of future problems. A video card which seems to regularly crash when it comes under load means that the card is moving beyond the limits of what it can endure, resulting in errors which cause the graphics driver to become non-functional, resulting in either the crash of an application or, in some rare cases, the entire operating system. While high temperatures and a defective fan hold the potential for problems, instability shows that there are already problems happening, although they may not yet be fatal.