Cross-pollination
Seeds saved from hybrid cultivars will not "come true" (resemble "mom") when planted out the following season. Seeds saved from non-hybrid (open-pollinated) cultivars of plants that normally cross-pollinate- cucumber, muskmelon, squash, pumpkin, pepper, corn, basil, etc.- may produce off-types when planted the following year. This occurs typically because of cross-pollination between different cultivars of the same species. For example, one may grow two or more different open-pollinated cucumber cultivars and save seed from the one that performs best. Unless the plants were hand-pollinated or screened to exclude insects, it is very likely that pollen crossed back and forth between the cultivars. Therefore, plants grown the following year from saved seed will express the combined traits of two different cultivars.
Note also that there are several types of vegetables (yellow crookneck, zucchini and acorn squash, pumpkins) that fall into the same species- Cucurbita pepo. These different crops will all cross with one another. This accounts for some of the bizarre-looking squash-like fruits that grow on plants emanating from compost piles.
Cross-pollination occurs between neighboring gardens as well. Your neighbor's garden may have a big effect on your plans to save vegetable seeds. And cross-pollination can also occur between species. For example, there may be considerable crossing between the five different cultivated species of pepper within a garden (e.g. Habanero pepper with Serrano pepper.)
Seeds or plants mislabeled
Occasionally, gardeners find that the plants growing in their gardens do not match up to the seed packet or transplant label description. In other cases, fruits may not appear true to type if old, low-quality seed was planted.
Seed saved from hybrid cultivar
Seed collected from F1 hybrid cultivars and planted in the following year will not produce plants identical to the F1 hybrid. Instead, one will see a wide range of characteristics expressed in the daughter plants that derive from the two inbred parents used to produce the F1 hybrid. In short, seed saved from hybrids does not "come true" when planted the following year. This may prove interesting to some gardeners and disappointing to others. It is best to only save seed from open-pollinated, non-hybrid cultivars.