My squash is doing the same thing! I thought it was because of lack of pollenation, but there were bees buzzing all over them this morning. It is also happening to my zucchini, but not as bad.

It is likely lack of pollination. If the weather has been cloudy or cool, the insects that do the pollinating may have not been working the flowers. (The first flowers that form on the squash vine are male flowers--they produce pollen and no fruit. Next come the females; the bees and insects must visit first the male, then the female flowers.) You can improve pollination by hand-pollinating: pick the male flower, remove the petals, then twirl the male directly on the stigma of the female flower. One male flowers can pollinate several females. Hand pollinate in the morning before flowers close in the afternoon.
Here a problem link:
http://www.harvestwizard.com/2009/05/squash_squash_growing_success.html

Here is a link that might be useful: HarvestToTable.com

Should you remove the small squash that aren't growing any larger? If so, how long should you wait before you remove them - just to be sure they really aren't going to grow bigger?

It's also possible you haven't gotten any male flowers yet. I'm getting only female flowers so far on my two summer squashes. But I can see male flowers on the way.
Go ahead and pick the failed fruits, or leave them there, it matters not.

If you want to be sure to get fruit, you may want to hand pollinate. Maybe the bees are busy with other plants. Most of the bees visiting our gardens this week are working the lacecap hydrangeas which are in full bloom. The hydrangeas are covered with bumble bees and other of the smaller bees. Fun to watch.

If you have only a few plants, hand pollinating is not much trouble. I have noticed fruit that is pollinated starts growing (swelling) very quickly. I think you should be able to identify the failed fruit in one-two days after the blossom closes.

Thanks for the advice - I guess I will look a little closer at the flowers and squash. We have had so much rain the last few weeks I just wasn't sure if that might be causing something different than I've seen before. I have tons of 2-3 inch squash and lots of flowers so maybe all is not lost.

This is my first year growing a garden my yellow summer squash is doing great but I have realized that I was not getting full grown squash! It would get about 2-3 inches an dies! Well after doing research I don't have very many male flowers! I have self pollinated all I can but so far I only have 1 squash an 22 dead little baby squash! Is this normal?