Empty Standing Water
Rain might collect in out-of-sight places, such as saucers beneath pots or a weeding pail left in a corner beneath the eaves. Mosquitoes breed in such shallow, undisturbed water. Mosquitoes carry the West Nile virus, which can be fatal to humans and pets, so ensure that your yard doesn't offer them any good spots to lay eggs.
Collect Rainwater for Houseplants
Even if you don't have a dedicated rainwater harvesting system, you can collect a bucket or two dripping beneath the eaves. Houseplants thrive with a drink of rain. During a rainstorm, watch where most rain runs off your roof, and consider adding gutters and/or a rain barrel for collection. Use the water within a few days so it doesn't invite mosquitoes.
Watch for Spider Mites
These tiny eight-legged creatures like dusty conditions. They are difficult to see, but tell-tale webbing gives them away. Hose off plants with a blast of water after windstorms to control any mites.
Skip Scheduled Watering
If rains are heavy, it's possible to conserve water and skip a scheduled irrigation. Water-logged soil isn't good for roots, either, as they need oxygen to thrive.
Correct Storm Damage
Prune broken limbs as soon as possible after storm damage. Use the 3-step method to remove large, heavy limbs. This prevents bark on the underside of the limb from tearing down the side of the trunk. Texas A&M Extension provides a publication with pruning illustrations at: http://aggiehorticulture.tamu.edu/extension/pruning/pruning.html.