I have 3 cucumber volunteers in my tomato bed. Either because I had cukes growing there last year, or more likely because I used my homemade compost that probably had rotten cukes thrown in last summer. Wondering if I should move the cukes or leave them to mature among the tomatoes. Also, if I had pumpkins growing near the cukes last year, what is the chance that these 3 plants will be weird "cukekins"?
If you are 100% sure of what kind of cuke seeds that you have been growing and they are open pollinated and there is no chance of any other kind of cuke seed getting mixed in, then I would move the cuke plants but be extremely careful because cukes do not like getting their roots disturbed and typically don't like being transplanted. Copy and paste the link about crossing between cukes and pumpkins: http://www.ipm.iastate.edu/ipm/hortnews/1996/8-23-1996/crosspol.html
Personally, I would not try to transplant the cucumbers. As fishhunter said, they do not like to have their roots disturbed.
I have had melons volunteer amongst tomatoes and both have done fine. I suggest you either pull out the cucumbers, or let them wonder through the tomato vines and see what you get.
I've transplanted cukes; it's not so bad if you have tons more than you need, but if you want them all to live I wouldn't recommend it. (On average about half of mine lived.)
I would think cukes would do OK interplanted with tomatoes; the cukes won't compete with the tomatoes at all, and the tomatoes will shade the cukes some, but cukes are more shade-tolerant than most garden veggies and shade can even help them in high summer or during a drought.