Most of the shows we go to don't have electric hook ups so we use our generator.  At one of the locations we do show at there are hookups and the cord from our trailer (three prong with a ground and two offset prongs) fits into the hookups.

This weekend we were at our state horse show and using some hookups that looked very old.  Not sure what type of connection the electric box had but it didn't match our plug.  I have an adapter that takes our trailer plug and converts it to a standard 110 plug, which the box had, and we plugged in this way for 4 days with no issues.

For future reference are the electric hookups usually going to have a standard 110 plug a the various places we may need to hookup?  If so is it safe to take the big 30 amp plug and use a convertor to hook it up to the standard 110?

What you are saying is the box had a standard 20 amp 110 outlet that you put an adapter on your trailers 30 map 110 cord and plugged into it?   There is no problem with this as your cord is rated for the higher amperage than what the outlet was delivering

A 30 amp plug looks like this

http://www.bing.com/shopping/30-amp-125v-replacement-plug-s078-558416/p/1046334CCFFFC02E5006?q=30+amp+plug&lpq=30%20amp%20plug&FORM=HURE

If your cord is rated for 15 or 20 amp and you are plugging it into a 30 or 50 amp outlet, then you run the risk of having more power than the cord is rated to handle.

Here's one that would serve .. Big Money though ..  All of $7

http://www.harborfreight.com/7-function-digital-multimeter-92020.html

Correct, I had the 30 amp on my trailer and used a convertor to make it the standard 110.   I guess the only risk I run is that the 110 outlet doesn't have enough amps to run my trailer?

Don't get confused with Voltage vs amperage.

110v can come in 15 amp, 20 amp and the 30amp ( like your cord)  that is why each version has a different plug.

Your A/C unit probably needs 18-20 amps to start up. So a 15 amp service would not have enough power to run your a/c.

A 20 amp service may have enough amp to run your A/C but not run your microwave at the same time as your A/C

A 30 amp service will have enough amp to run multiple appliances but may over load a thin wired extension cord  i.e. a 14 or 12 guage cord.   14guage cord = 15 amp service  12 guage = 20 amp service and 10 guage cord = 30 amp.  This why you see most trailers with a minimum of a 10 guage power cord to connect to the shore power.  Too heavy a cord is only a problem in that it is heavy and stiffer than lighter cords.  Too light a cord will over heat if heavy amperage is run thru it and may melt.

Exactly, But I was thinking more in the terms of the standard 25 foot length cord that most LQ or RVs come equiped with.  Very few trailers come with more than 25-30 foot coiled up in that little box on the side of the trailer.