If I grow multiple varieties of tomatoes right next to each other and I plan to save the seeds. How worried should i be about cross breeding?
Yes! and with other things too.You don't plant zucchini next to yellow summer squash. You can get lovely yellow and green squash. cucumbers and melons don't do well too close together either. dooley
You need to bag the blossom you are saving the seeds from before it is pollinated by any other pollen. pollination can occur from insects or just on the wind. Otherwise I would suggest getting new seeds that are specifically what you were planning on growing. What were you planning on growing? I may have a few I could send you, it just depends on what you want. Same goes for squash, if you plan on saving the seeds keep them separated by 50' or more. They are dependent on insect pollination. If you are saving the seeds hand pollinate them and bag the blossom to keep it pure. You do not want your summer squash pollinated by winter squash and plan on eating it next year when you grow the seeds.
Tomatoes are self pollinating. Just place a small paper bag over the blossom cluster before the color of the petals show and tap it every couple days to make sure the flower has enough movement to drop the pollen from the anthers onto the stigma. if the bag gets wet from rain (dew won't hurt it, it will dry fast from that) change it or after the tomatoes are formed put a ribbon on the cluster so you know which ones to save for seeds.
What varieties are you using ? Hybrids will not grow true from seed no matter what you do ! So no point in getting anything except heirloom varieties for seed saving.