Hi Philo,
Someone gave you wrong info. They probably meant to say you didn't get many squash because of no pollination. Squash, and others in the squash family, blooms are either male or female and need an insect to carry pollen from bloom to bloom to ensure pollination. Sometimes not enough insects are around to pollinate. Also sometimes the plants seem to develop all or almost all the same sex flowers at certain times so even if insects are around chances of pollination are lowered.
You can replicate insect pollination by taking a male bloom in the morning and lightly rubbing the insides onto female blossoms. The male ones have nothing at the base the flower. Female ones have an undeveloped squash at the base.

Cross pollination happens when you grow two squash of the same species. An example is Acorn Squash, Zucchini and the little ornamental gourds(not real gourds like a birdhouse gourd) are all Cucurbita pepo. They will cross. They will not cross with other species. Like a Hubbard squash, Cucurbita maxima, will not cross with a Cucurbita pepo type squash. So when growing squash as long as the second name does not match, you can grow different types without worry of crossing if you wish to save seed.
And squash do not cross with melons or cukes. You only have to worry about cukes crossing with cukes and melons crossing with melons.
I hope I made sense,
Remy

Here's a link to a thread on hand pollination of squash. If you wish to grow more than one squash of a given scientific family (closer than about 1/2 mile apart), then you should hand pollinate. It's not hard. Hand pollination can improve yields if you have a lack of pollinators. If pure seed in isn't important to you, then you can do the hand pollination and simply forget about covering the flower afterwards.

George
Tahlequah, OK

Here is a link that might be useful: Hand pollination of Squash

George,
I wish I had know you posted those great pics before! I'll definitely link to it next time I get a squash question. It is much easier to understand with pics.
Remy

I just figure that the technique should be freely available and, pictures are essential for learning. I'd like to see MANY more gardeners using the technique.

George