What are the most common spring-time allergies?

Tree pollen. The most common spring-specific allergen is tree pollen. Grass typically pollinates in the summer, weeds in the fall. Perennial allergens are around all year, and include pets and dust mites.
Trees. Trees pollinate in the spring, and which ones are most dominant varies by region. Grasses pollinate in the summer, and weeds in the fall. There are very few things that pollinate in the winter, those tend to be at more southern latitudes.