Most cucumber plants have seeds and depend on bees and other pollinators for well-formed, healthy fruit. Seeded cucumber varieties will not generally be affected by cross-pollination with other seeded varieties, or with similar vine plants like melons or zucchini.
Seedless, or parthenocarpic, cucumber varieties are another matter. These plants are usually grown in hothouses where bees are excluded. If they do cross-pollinate, the fruit quality degrades. Solutions for home gardeners include growing seedless cucumbers in an enclosure without access to bees, planting only seedless varieties, or leaving the seedless growing to the pros. If seeds bother you, there are plenty of varieties with small or minimal seeds. Or, you can just remove them before eating!
What types of cucumbers have you tried growing? Please tell us about your experiences.