Cucumber (Cucumis) and squash (Cucurbita) are not the same genus so will not cross. But summer squash, winter squash and some gourds are Cucurbita and will cross.
All peppers are in the genus Capsicum so will cross.
You won't notice the cross unless you save seeds and grow them next year.
But if you grow more than one type of corn and they cross, you will see the results in the corn this year as you are eating next years seed fresh. Its easier to tell the difference between corn seeds then pepper seeds.