Are there any types of cancer that are more common in people who have celiac disease?

Only certain cancers. Population-based studies have confirmed that patients with celiac disease are at increased risk of mortality. However, they do not seem to be at an increased risk only to lymphoproliferative malignancy (of lymph nodes) and gastrointestinal cancer. A gluten free diet may reduce those cancers, possibly reduce the increased mortality as well.
Yes. Celiac disease, especially if one has symptoms or small intestine inflammation/damage, does increase one's risk of small intestine cancer (adenocarcinoma and lymphoma). The increased risk may go back to normal if one stays on a completely gluten free diet and stops having intestinal symptoms for many years.