The generally-accepted minimum for most tarps is the length of the hammock plus a foot. It's probably better if it's plus two feet (and how sharply the tarp tapers at the ends plays a large role in this, too).
There are three major styles of tarps: rectangular, hexagonal, and asymmetric diamond shaped.
Rectangular tarps are the simplest as far as design goes; the advantage here is total coverage. If you get one that is long enough and has the proper tie-outs, you can close off the end corners into "doors" that will block wind and precipitation. The wind-blocking comes into play the most during the winter, which makes these types of tarps popular with those camping in cold weather.
Hexagonal tarps are just rectangular tarps that have had their corners cut off. These types of tarps are a compromise between weight/bulk and coverage. They tend to give good coverage to a hammock (since the hammock tapers towards the ends, it needs less coverage there), while saving weight. The downside is that you can't close off the ends without additional equipment (though a poncho and some line fixes this right neatly, in my experience).
Asymmetrical diamond tarps are as minimalist as it gets. They're generally the lightest tarps out there, reducing pack volume at the same time. They're hung with the long axis running the length of the hammock and the short axis across the hammock, usually with the points at left shoulder and right knee to allow one to lay asymmetrically in the hammock and still have overhead coverage. These can be used in extreme weather (Sgt. Rock has a story about hanging in a hurricane with one of these), but require skill to set up well enough to avoid being wet under such circumstances.
So, really, what you need to balance is how much coverage you need versus how heavy a pack you're willing to carry.