I've always heard that planting annuals is a waste of time and money since you just have to buy them again next year. Where this might be true in some cases where the plant doesn't grow and propagate well in your area this doesn't have to be the case. One of the best things about annuals is that they spread so easily by seed. Otherwise we would soon have none left since they die every year.
Some annuals that I have in my garden are basil, cilantro, lettuce and onion which are all prolific seeders. Although I harvest most of the seeds, there are still many others that produce the next year's crop.
Some less self seeding plants are your peppers, tomato, melons, squash and cucumber. These have to have the fruit eaten and the seeds scattered in the process or saved by the gardener for the next year instead of the plant just dropping seed.
It's well worth the little bit of time it takes to successfully save seeds. Although we live in a fast paced world seeds need to be dry before storage. This can takes days if the air is too humid. Make sure you store the seeds in airtight containers. If you notice mold growing in one of the containers you might be able to save some of the seeds still if you catch it in time.
First, make sure the seeds you are trying to save had no mold on them. I like to use plastic bags which keep seeds spread apart and limits the ability of mold to spread. If they started to mold I wouldn't bother. if you do use plastic bags it's easy to cut out the area that doesn't have the mold and start over with drying. There was too much moisture.
After a few seasons you should be able to tell when the seeds are ready for storage. Note however that every type of seed is different even if the difference is only slight.