Is there some combination of keys I can push to make my own telephone (or another extension in the house) ring?
This is known as “ringback”. You dial the correct number and hangup, and the Switch at the Central Office will call you back. There are different numbers for different carriers and different areas.
How would I do that in Austin, Texas?
gotta be part of the phone company. or know the secret handshake. sorry.
In most areas, it’s 550-(your number) or 551-(your number), where (your number) is is the last four digits of your telephone number. For instance, if your phone number is 555-1234, the ringback number is either 550-1234 or 551-1234. Ater you dial it, you’ll hear a tone, if you have the right one. Then switchook the way you would to get a call waiting call, and hang up. If you’ve done it right, your phone should ring a few seconds later.
I beg to differ, though it is possible it’s those in some areas. It isn’t that in areas I’ve known about (which is mainly northern and southern california, so admittedly not a huge experience base)
Perhaps I shouldn’t say this, but you can find tables for what it is in various areas with google and some trial and error. (much of what you’ll find is very old info.)
Here it’s like what Q.E.D sez, but with 999. Or it, was. It stopped working for me a while ago. T’was very useful too, in case you happened to take apart your telephone to see how it worked, and wanted to be sure it was still ringing when you put it back together. 
P.S. - In case you are both in Europe and stupid, I should note that the 999 prefix may get your phone to ring shortly after you hang up, but that you won’t like the associated consequences. 
Um, I can dial my own number (exactly) and hang up right away and the phone will ring.
Lonely night, maybe I’ll call myself…
What whuckfistle says used to work here but not anymore.
Which are…?
I think that the same a 911 in the USA!
Not quite. It’s supposed to be 112 in all of Europe nowadays. However, 999 used to be the emergency number in England, although I believe that it has now been deprecated.
In order to answer the OP, I can add that the self-dial code in Sweden it used to be 0058 (stopped working about five years ago).
Here in Florida, Tampa and the surrounding areas at least, all you have to do is dial your own number and hang up.
I dont think 999 been’s replaced totally by 112 here. No-one really thinks of 112 as the proper number. If they got rid of 999 totally, houses would burn down, criminals wouldn’t get arrested and the injured would remain so.
Cheers, Harry
I`m guessing that that is their version of 911…?
Whoops, hamsters…
This site says it’s 95 followed by the last five digits of your phone number.
my question is, why would you want to do this? sheer curiosity? boredom? trying to fake out everyone in the house?
You want to test the ringer in your phone, or make sure that you are able to receive calls and not just send them. This is probably leftover from way-back-when the big bad phone company owned the telephone in your house and needed some method of testing it to see if it would respond to the ringer signal.
Not that I can help you with your local number, but if you can’t find out the correct ring back number, you can set a phone alarm and have that ring you back. I’m assuming you have a phone alarm service.
Here in Bombay, I have to dial 161 or 162 to have the phone call me back. I use it sometimes if I need to call someone in the other room and I’m too lazy to shout out 
An interesting phone fact: It is possible, atleast here, to call up another number without using the buttons at all. Just use the hook to dial the number. You have to be good and it needs a bit of practice. Press the hook like dat-dat-dat for 3, dat-dat-dat-dat for 4, dat-dat-dat-dat-dat for 5, etc. with a short pause between each number. It basically simulates a rotary dial. I used to use it as a kid when mom or someone would lock the dialpad.