Star codes can be used to program you phone to do a lot of useful things. Other features, which may be free, can be set up by calling your phone company.
UPDATE 2020: This information is based on old landline phones, which few people use anymore. When I posted this back in 2011, landlines were still a "thing". How times have changed! We dumped our landline years ago for a VoIP line, and now even that (and wired internet service) are gone. We've gone entirely wireless. So this posting is of historical interest only, I guess.
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Most people know that you can hit *69 to see the number of your last incoming call. This is one example of a "star code" or Vertical Service Codes, and there are a large number of them.
There are a number of sites on the Internet which list these codes. For example, this AT&T guide lists most of them. This independent site has a short list of them. This site provides a far more detailed list, which is also on Wikipedia. And of course, if you use AT&T VoiceMail, you may access this from a star code (*98) as well. Here are some easy-to-use instructions for AT&T Voicemail...I think they were just trying to see if I was paying attention. I was.
Not all of these codes may work on your phone - depending on provider or service level or service package. You may have to try them to be sure or search online for star codes for your local phone company, or call customer service or read the user's guide (if they sent one) when you started service.. And be sure that your phone company does not charge for using codes before you try them. Depending on company and plan, some star codes may incur charges, although this is becoming more rare these days.
There are some codes that are useful for nearly everyone. Callback Service, (*69) is handy to see who just called you, if you miss a call. Call forwarding (72# on my AT&T line) is handy if you are going on vacation and want your calls to forward to your cell phone or other phone. Call forwarding-don't-answer ring control (*47) is another fun one, as it will forward to another phone if you don't answer the first phone, after a programmed number of rings. In this way, people can call your home phone, and if you don't answer, it will forward to your cell or office.
Repeat dialing (*66) will continue to dial a busy number until you get through. This is a lot cheaper than some of those services offered on the phone sometimes (wanting $3 for this service!). With the advent of VoiceMail, busy signals, however, are largely a thing of the past.
Anonymous Call Rejection (*77) will generate a nice recording to people who try to call you with their caller ID blocked. When you think about it, there is no reason anyone should block their caller ID (which you can do with another star code). So just play them a recording that says "this phone does not accept calls from phones with caller ID blocked"). NOTE THAT *77 may call the State Police on some cell phones, so be sure to check before using it on a cell phone!
Call Blocking (*60) allows you to block any phone number you enter, or by pressing #01# will block the last incoming call. This is great for annoying telemarketers or if you get harassing calls or just the same damned drunk mis-dialing your number again and again.
There are other services you can use on your landlines and wireless lines, that are free as well:
Slamming & Cramming: I wrote about this before. In the old days, slamming was quite common - you'd get a weird phone call and when you answered the phone, they would say your name and you would say, "Yes?" and before you knew it, your long distance provider was Sprint. Slamming occurs less often now, but cramming is the new gag. You go to a website that says you can get paid for doing online surveys! (with an exclamation point! of course!) and they ask for your cell phone number. Under the ToS you glazed over was permission to add "line guard" to your phone service - a nonfunctional service that does nothing but add $9.99 to your phone bill -forever. And the phone company cannot take it off - you can only ask the people who put it there to stop, and of course, since it is a negative option deal, they don't. Avoid cramming by having your phone lines locked from 3rd party services being added.
900 Call Blocking: This is a free service of the phone company. 900 numbers and 976 numbers are basically scams that for some reason the government felt we needed to have. If you dial a 1-900 number, you may be charged several dollars a minute for a phone call. Most of these numbers are porn numbers - dirty chat lines and the like. Others are pure scams. You get an e-mail that says "Call this number for more information!" and when you call, they make you listen to long recordings so that rack up tens of dollars on your phone bill.
You can block these numbers, so that no one in your family will call out (Children were targeted as part of these scams - and often called 1-900 numbers with promises to talk to their favorite television characters, etc.). For AT&T you have to call customer service to set this up. Usually, it is a good idea to do this when you order new service - they may in fact ask you.
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Your landline and cell phone have a lot of electronic services - most of which are free - that you can use intelligently to save money on your phone bill. For example, if you have a cell phone and you have a land line, rather than paying for Voicemail service for your landline (or using an answering machine), you can call-forward your landline to your cell phone, where callers will then bounce to your free VoiceMail. VoiceMail messages can then be retrieved from your landline, for free, without using your cell minutes. This could save the hassle of using an answering machine (which generates busy signals when in use or if you are on the line) and also save the $7 a month they charge for landline VoiceMail.
If you think creatively, you can do a lot with just the free services they provide with your phone. And yet most people don't even know they have these!