The answer is a highly subjective, according to both the wine and the drinker. Generally, dry white wines have the shortest life once opened. I find they lose their character after even one or two days, especially cheaply-made, oaky New World whites. (Whites with good acidity and lots of character from Burgundy are an exception.) For reds, I think that most start to slip after two days, though again it depends on how well the wine was made. There are always exceptions.
Sweet and fortified wines, such as icewine, port and sherry, have a longer life because of their higher sweetness and/or alcohol, both of which act as a preservative. I still like most opened icewines after three to four days; ports from one week to four, depending on their quality. You can extend the life of any opened wine by giving it a few squirts of liquid nitrogen, such as Wine Preserver, a spray can sold in many liquor and wine accessory stores. Another trick is to pour your remaining wine into a clean, empty half bottle size and cork it. This also minimizes the amount of oxygen that can affect the wine. Some drinkers don't mind a wine that's still 60-80% there in terms of its character; others want the full expression or nothing. I tend to err on the latter side of the ledger.
And then again, I never seem to have to deal with the issue of an unfinished bottle of wine! Share your open-bottle stories with me at www.nataliemaclean.com.