I purchased squash and cucumbers in peat pots from a local store. Each pot has 3 small plants sprouting. Do I plant it as is or do I thin them to one plant per pot before planting?
You can go either way. Vining plants like this are often planted in a group and then thinned. Or not, if you have space to head them off in different directions and let them all grow.
The safest route is to plant the pot as is and thin, if you choose to, when the plants have settled in and you can confirm that all will survive the transplanting nicely.