In determining what kinds of exercise are compatible with yoga, it's important to first identify what your primary challenges are. For many people, the most glaring challenge is flexibility, while for others the big hurdle is strength. If your main concern with yoga is to increase your flexibility, then it's probably true that activities such as weight training, which tends to contract muscles, or running or biking, which can lead to tightness in the hips and hamstrings, may counteract some of the flexibility work you do in your yoga practice.
That said, one of the primary purposes of yoga is to help us achieve balance. Many people are under the impression that the purpose of yoga is to become flexible. This idea can be terribly misleading, as there are many practitioners who are already overly flexible, and who in fact come to yoga needing to increase their strength in order to stabilize and support their hyper-mobility. For someone who is already very flexible, cardio and weight training could be beneficial.
For someone on the tighter end of the spectrum, however, I recommend activities that are more likely to elongate the muscles. The two forms of exercise that I personally find most compatible with my yoga practice, on both a physical and a mental level, are walking and swimming. There is something about the quality and the rhythm of both that echoes the spirit of my practice and seems to complement the yoga on all levels.