Yes, it is done all the time. ;)

Tomatoes and peppers can cross-pollinate with other peppers and tomatoes but only in a limited fashion (approx. 5%) - they are self-fertile plants and 95% of the time each bloom pollinates itself.

However, it is important to note that cross-pollination is only an issue/concern if you intend to save seeds for the following year. CP does NOT affect the fruit on the plant, only the seeds.

Most of us who save seeds from open pollinated (heirloom) varieties don't worry about the 5% chance - it becomes and issue only if you are saving for sale or for pure variety trading. And, of course, seed saving from hybrids is pointless unless you are heavily into hybridizing so cross pollination isn't an issue if it is hybrids you are growing.

Dave

The Peppers and cucumbers will cross without row covered barriers (Re-may).You should stick with one var. of each if you want pure seed. (Peppers and Cucumbers) Don't worry about the tomatoes unless they are Potato leaved.

In typical fashion, Dave has explained it very well and I agree with everything he said. In re-reading your post, you use the phrase "....I'd like to know if I can grow different varieties without cross-polination issues.". If Dave didn't address your concerns, please let us know what those cross-pollination issues are.