The One Ring, as not just the product of Sauron's craft but the emobiment and carrier of much of his will, simply represents the power of Evil. This doesn't make the situation very clear, because the very nature of evil in Middle-earth is hard to define, fully. At the core of all evil intent, however, is desire -- the desire of and for self-gratification rather than selflessness. All the people who choose to possess the Ring do so for the gratification of their one overwhelming desire: Boromir for the protection of Gondor and his own renown, Isildur as an heirloom and "wergild", Saruman for the knowledge that it will bring him, Sauron for the power to make his desire the only one in the world capable of being realised (rendering the world a stage upon which only his will can be enacted).
Even those who reject the Ring recognise that in order to do so they must reject their own desires: Sam for a garden and sunlight, Gandalf for the "strength" to end Sauron's reign, Galadriel for a kingdom of her own.
It is through these choices that the Ring comes to represent a non-particular, even Universalised form of Evil. It promises people whatever they want, just to try to trick them/compell them into choosing their own desire for [whatever. In other words, it tempts them to make an evil choice by turning away from the Good.
I suppose the best way to answer the question of what the Ring represents is simply by saying what it is not: it is the evil that results when one turns from Good; it literally is the shadow cast by an ill-will.
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