The obligatory way to explain the "burner" phone is by mentioning The Wire, one of the greatest television shows of all time that almost no one watched.
The show is streaming on HBO Now/GO and Amazon Video, so catch up when you can. But for the uninitiated, a burner is a no-contract, prepaid mobile phone, usually an ultra-cheap handset you buy in a store (with cash, for privacy), activate with a call or online, use for a while, then discard. The throwing away is the "burning" part, but tossing it is optional, since these days you can "top off" the minutes on a prepaid phone and keep using it.
There are a lot of good reasons to not hand out your personal phone number. Perhaps you're buying or selling items on Craigslist, managing an Airbnb listing, or online dating. With a burner, you don't have to block a person from your permanent phone—or get a new number—later.
All of which is great, but when you pay big bucks for a smartphone with expensive monthly carrier fees, you may not want another handset. Thankfully, there are a lot of ways to get an extra, temporary phone number that works with your iPhone or Android smartphone. You can use them to make calls or send texts (even with photos) and get messages back in return. This isn't like using *67 or #31# before a call, which shows you as Blocked or Unknown. Using those tricks, people can't easily call you back, not even with *69 (look it up, kids). The services below make a point of showing a temporary number when you call, so communication can happen—until you want it to stop (or run out the clock on a number).
Note that there are some serious drawbacks with these services. The biggest is that you typically can't use them to call 911 for help. Some services build that particular limit into their terms of service—they don't want to get sued when you call emergency services and get bupkis.
Second, the companies behind some of these solutions have a very limited number of phone numbers to use. Research from 2014 found that some companies recycle numbers quickly, meaning you could be on the receiving end of calls you don't want, from those trying to reach someone who previously had your number.
Now, if you've finished watching The Wire (seriously, season 4 in particular is amazing), get ready to access some apps and services that will maintain your privacy.
Burner
Seven-day trial with 20 minutes of talk and 60 texts; unlimited texts, minutes, and pictures requires $4.99/month Premium subscription.
Burner grabbed the best name in this area and lives up to it. Limited to US and Canadian numbers, the service has numbers that usually expire after a certain time period. You pay for them with in-app purchased tokens. If they lapse, they're burned. The newer premium subscription gives you a permanent second number.
When you make a call via Burner, it actually is your smartphone calling Burner, which in turn places a relay call to the number you want to reach. The steps are spelled out as you make a call, so you're not confused. A Chrome extension helps you manage numbers, but it doesn't do calls or texts on the desktop. The app lets you change the color scheme and even locks out users without a PIN code.
Burner can directly integrate with apps like Dropbox, Evernote, Slack, and SoundCloud to help you with sharing or storing items online. For example, make sure all voicemails left on Burner by certain contacts get stored in Evernote.
Hushed
Five-day trial, then $1.99 for seven days or $3.99 per month with limited calling/texts.
Hushed is a lot like Burner, but available in over 40 countries. If you're worried about the minutes left on your actual mobile phone contract, Hushed goes for VoIP, meaning it'll default to making calls over Wi-Fi rather than the data network, when available. Text communications between Hushed users is all free, and they auto-delete after being read.
Too
No trial, costs $1.99 per 30 days. You're charged by the minute (3 cents) and per text (8 cents), as well.
Too provides a simple, single, extra number for the US, UK, and Canada. It supports MMS/picture messaging in the latest version, as well as emoji and deletable voicemail. You can use Too on up to five iOS devices with the same number supported on each. This number is semi-permanent—as long as you pay for it, it stays yours.
CoverMe
No trial, extra numbers start at $4.99 for 130 texts and 130 voice minutes.
Best known as an app for providing secure communications over VoIP between users, both voice and text, CoverMe also offers extra phone numbers for US and Canadian users, which can be used to receive calls.
Packages aren't cheap. Unlimited texting is $99.99 and comes with 3,000 voice minutes. The lowest tier is $4.99 for 130 texts and 130 voice minutes. CoverMe has a very limited pool of numbers. I couldn't get one in my home area code nor any NYC area codes. That said, CoverMe has lots of tools for privacy beyond calling and texting. It also features a vault for holding images and documents you don't otherwise want seen on your smartphone, which you protect with a PIN code or, if you've got a newer iPhone, your fingerprint.
Google Voice
Free
The main purpose of Google Voice is to provide you a single phone number, entirely free, that rings on all your numbers. That way, if an important call comes in, it can ring your cell, your home number, your office number, and others all at once—you pick up the one you want. (This is less and less an issue in the one-phone-per-person mobile world.)
However, the Google Voice apps also feature dialers so you can call or text out with your Google Voice number—the recipient will see it and if they return the call, you'll get it at the preset numbers (or get a voicemail with full-text transcription). Remember, if you have a Google account, you've probably got a Google Voice account already. A recent redesign doesn't hurt.
ZipSIM
Starts at $25 for 7 days of talk, text, and 500MB data plan. International long distance calling is extra.
Another thing you see in the movies a lot: people swapping out tiny SIM (subscriber identity module) cards in their phones. That's the chip in your phone that makes it totally unique to you, giving the phone its ID and number, sometimes even storing contacts. ZipSIM (formerly Ready SIM) sells temporary-use SIM cards (in all sizes—check your phone before buying). The target audience is mostly people from overseas visiting North America, but anyone can get one, slap it in their unlocked T-Mobile-compatible phone, send a text to activate it, and have access for the time-frame and allotted minutes/data you paid for ahead of time—all with a new phone number. To keep it going, just "top up" (pre-pay) the account. Keep in mind, this SIM swap stuff can be a little trickier with an iPhone.