Go to Target or Walmart and buy a Virgin Mobile pay as you go phone and a minutes refill card (200 min. for $20), pay cash for both.

Next, you need a fictitious name (first & last), a fictitious address, but the address has to be valid, and a fictitious email. Make sure the address is not near your neighborhood.

You need a six digit security code, incase you lost your phone, or had to throw it away, so you can reactivate a new phone with the same number. Use a code that you can easily remember, don't use birthdate, SSN.

Call the toll-free number from a pay phone as far away as possible from your neighborhood to activate the cell phone.

Give them that information and the cell phone S/N, and when they ask you for a landline number just tell them you don't have one.

Lastly, give them number from the refill card to add minutes to your cell phone.

Your new hobby phone will be activated within a minute or two.

You maybe tempted to activate the phone over the internet, I suggest you don't, they will record your IP address which can be traced back to you.

Keep the cell phone locked, also use a 4-digit code you can easily remember, but hard to guess for anyone else. Lock the phone after each usage, this is very important, and do not store any personal info on it, or anything that can be traced back to you.

Be safe, and have fun.

Go to Wally World and buy a Tracphone or such with cash and authorize it using a land line and don't really give them any real information that can be traced back to you.  Also buy air time using only cash, no credit cards. Keep the phone in a safe place, turned off when you aren't using it.  I even take the battery out just in case the phone has a warning alert when the battery gets low.  Also if there is no battery in it and the phone is found it makes it harder for anyone to check any history of calls made or received.  some might think I'm paranoid, but I like to be careful.

What's the best way to get a throw away "hobby phone" with an untraceable number?

I used a fake name & it came up with a defaut address in Florida which I assume is Company HQ!   I shut it off when not in use.  After use, I delete all sent & recieved calls.  It means I must re-enter a number when making plans but offers a layer of delay/protection in case it is unfortunately found.  I hide it pretty well.  
NO phone it totally untraceable.   If you MURDER someone, LE will find the towers it's been used on.   I'm not going to murder anyone.  
skb

... I would have done it this way:

1-Buy a tracphone and top card and pay for them with cash.

2-Activate the phone from an unsecured wireless network. You can go to www.openwifispots.com to find free wireless hotspots in your area. Many McDonalds and Starbucks have them. You can activate a tracphone without giving a name or any other personally-identifiable information. Other prepaid cellphones may allow this as well.

3-When your minutes run out and it's time to add minutes to your phone, buy a top card (with cash) and add the minutes online, again from an unsecured wireless network. Better yet, don't replenish the minutes. Instead, destroy the phone and buy a new one.

You might also want to set up a hobby e-mail account. You can set up an account on AOL (http://mail.aol.com) without giving any personally-identifiable information. Again, do it from an unsecured wireless network.

one really needs a hobby e-mail account, not linked to your main account.   Unfortunately, it will be traceable by IP address.  Most HotSpots use filters so adult sites can not be visited.  Do not use  company equipment or wireless with your personal laptop (unless you own the company).  The company has the right to moniter their network...  guys have been fired for this!  Except for the cost, a personally owned mobile link would work.  Using a personal connection at home is ok IF you set your system to clean up after you.  Some use a different brouser.  Always log out of everythng & shut the system down (even if you must lie & "accidentally" do so).   Never access adult sites when there is anybody else in the building.  
I shut off any noise I can so I can hear vehicles in the driveway...  long before anyone can get in the door.
skb