Short answer: yes. Some home gardeners think they have to start anew when it's time to plant again in spring. But unless your container (and soil) held a diseased plant, you can certainly save some money and reuse the soil for this season's plants.
Commercial potting soil is technically not soil at all, but a sterile mix of filler ingredients and organic matter. Oftentimes, you'll find a bag of potting soil labeled as "soilless," which only adds to the confusion as there isn't any soil in there at all. Some common ingredients in potting soil (sometimes called potting mix or sterile growing medium) are peat, coir, perlite, sand, composted bark, composted chicken manure, worm castings, spent mushroom compost, and ground limestone. Each of these elements plays a part in aiding water drainage or water retention, maintaining the proper pH level for sensitive plants, or delivering nutrients to the roots.
By the time your container plant has gone through a complete life cycle, the soil it's in has been depleted of any and all nutrition, leaving behind only the filler ingredients that hold it in place. Before you simply plop a new plant in the soil, you'll need to perk it up to ensure a successful new growing season.
First, dump the soil into a large tub and fluff it up with a trowel or fork. Remove any weeds, seeds, roots, or remnants of the previous plant, but leave the earthworms if any have wiggled their way into the container.
Add well-aged compost to the soil at a ratio of 25% compost to 75% soil. Compost will rejuvenate the medium with a good dose of NPK (nitrogen, potassium, and phosphorus) that your plant needs in order to thrive.
If your potting soil feels a little heavy (as compost tends to be dense), add in a little perlite until the soil feels light and fluffy. Balance is key; too much perlite and water will drain too quickly from the soil.
Mix in the recommended amount of an all-purpose slow-release organic fertilizer. An all-purpose fertilizer is well balanced and formulated for flowers, vegetables, and shrubs. You'll only need to amend your potting soil once a season, so don't skip this step.
Fill your container with your newly refreshed potting soil, water it well, and plant! If you grow vegetables in your container, it's a good idea to practice crop rotation among your containers each year by not planting the same thing in the same soil for at least two or three years. This helps avoid the spreading of diseases to new plants.