There is an increasing amount of research being done on the effects of meditation on the brain (see this article in Time on one recent application of this research). The following are a good sampling of some of that work. Some of them are a bit technical, but some of it should be understandable (particularly the videos).
Meditation and the Neuroscience of Consciousness
Antoine Lutz, John D. Dunne, Richard J. Davidson
Regulation of the Neural Circuitry of Emotion by Compassion Meditation: Effects of Meditative Expertise
Antoine Lutz, Julie Brefczynski-Lewis, Tom Johnstone, Richard J. Davidson
Long-term Meditators Self-induce High-amplitude Gamma Synchrony During Mental Practice
Antoine Lutz, Lawrence L. Greischar, Nancy B. Rawlings, Matthieu Ricard, and Richard J. Davidson
Attention Regulation and Monitoring in Meditation
Antoine Lutz, Heleen A. Slagter, John D. Dunne, and Richard J. Davidson
Neural Correlates of Attentional Expertise in Long-term Meditation Practitioners
J. A. Brefczynski-Lewis, A. Lutz, H. S. Schaefer, D. B. Levinson, and R. J. Davidson
Alterations in Brain and Immune Function Produced by Mindfulness Meditation
Richard J. Davidson, Jon Kabat-Zinn, Jessica Schumacher, Melissa Rosenkranz, Daniel Muller, Saki F. Santorelli, Ferris Urbanowski, Anne Harrington, Katherine Bonus, and John F. Sheridan
Daniel Goleman has written a more 'popular' piece on compassion meditation and happiness:
Finding Happiness: Cajole Your Brain to Lean to the Left
Two of the monks who have participated in Davidson and Goleman’s studies are Yongey Mingyur Rinpoche (author of The Joy of Living and, most recently, Joyful Wisdom) and Matthieu Ricard (“the happiest man in the world” and author of Happiness: A Guide to Developing Life's Most Important Skill) and both are good authors to read up on. Ricard has a very good Google presentation: Change your Mind Change your Brain: The Inner Conditions for Authentic Happiness. I would also suggest Philippe Goldan’s Cognitive Neuroscience of Mindfulness Meditation and Michael Spezio’s Mindfulness in the Brain. Finally, Richard Davidson has a lecture titled Be Happy Like a Monk (Part 1, Part 2, and Q&A).
Since I posted the entry on Zen Brain, the Upaya Institute and Zen Center has had a 7-part Science Meets Meditation series with Alan Wallace. I haven't had the chance to listen to them yet, but Wallace is a very familiar name in Ameican Buddhism, so it could be worthwhile.
The systematic research of the physical and psychological effects of meditation is currently on the uprise, allowing us to at least partially move beyond anecdotal evidence or traditional claims as to its effects.