I enjoy a lightweight, non-waterproof bivy for some conditions. The bivy allows me to camp on smaller ledges, ridges, or sandy areas less suitable for tents (especially useful when you are trying to minimize impact in desert areas by camping on slickrock), keeps dust, dirt, creatures, and wind out of the sleeping bag when sleeping under the stars, fends of dew and minor moisture, is easy to setup, and provides an cool aesthetic experience (see Andrew Skurka's many discussions of this). However, a non-waterproof bivy, while avoiding many of the issues involved with waterproof bivies, does not stand up to sustained rain. Unless you want to take the risk, a small tarp is the answer to this problem. Together, tarp and bivy can be a formidable combination in nasty weather, and if one ends up stuck in those conditions, tarps sometimes provide more practical living space than a single or double wall tent for the weight (especially if you hike with trekking poles, or string between trees).
According to postings elsewhere on this site, a tarp may also improve bivy comfort overnight by blocking radiation from the night sky that can cool the top surface of the bivy below the ambient temperature of the air, thus reducing the risk of condensation inside and outside the bivy. Apparently, trees can also block this radiation. I can't speak with authority to the range of conditions where this would make substantial real-world difference, but it is interesting to consider!
I know your question wasn't about bivies per se, but it is always useful to evaluate questions about gear based on the system within which they will be used. Evaluation of pros and cons may change with conditions, number of hikers, experience of those hikers, personal preference, etc. For example, I've seen some on this site who bring a tent and a tarp to provide more sheltered space when backpacking with children.