If I buy a prepaid SIM card with cash and insert it in my existing phone that I have previously owned, will my calls be traceable?
Thanks

Yes. Keep in mind, that there is a new measure now heading to congress where there will be no more such thing as disposable cellphones. What do I mean by that?

It means, you wont be able to use cash to pay for pre-paid phones and minutes anymore, you have to use a pre-paid card like a refillable one, or your banks debit/credit card. With the reload/refill prre-paid cards, you have to show your ID.

Expect the phone industry to fight this.  They are not stupid...

I used to work for a forensic software company. What it does is be able to obtain your SIM contact and call logs as well as every information on a cellular or smart phone. They sell their product to police and other organizations. If the police gets your phone, they can run that software on the phone and get everything you did on it. Your best bet is a CDMA LG phone or the latest phones available, no older models as they do not have those phones to test with nor the drivers to talk to the phone.

Same goes with hard drives on you computer even if you reformat the hard drive without an encryption software that can also wipe your hard drive.

Be safe out there my fellow hobbyists.

IMHO, one should not speak or text or e-mail anything which might be "misinterpreted" were it to be made public.  The presence of your phone number, e-mail, etc does not prove beyond a reasonable doubt anything untoward went on.  Requestes are best whispered to your lady when both are naked between the sheets.  

We are not spies, this is not the CIA.  Given enough motivation, the right warrants, virtually anything could be traced.  They tracked the CL Killer right to his appartment building.  Without recovering data, the location was all that was needed.

In most jurisdictions, pay for play is a misdemeanor.  (Just don't assault or murder anyone, all bets are off!)  Often misdemeanors must be actually witnessed by a LEO to prosecute (varies with jurisdiction)...  unless you confess, of course.  So tracing prepaid phones accomplished nothing, in the legal sense.

Keeping your personal business private from spouses & employers (add friends & family) is a different story...  and greater danger!  
By all means, if you are headed for divorce court, clean your hard drive...  but I hope you were not sloppy along the way.  
skb