The 3 local operators - Swisscom, Sunrise, and Orange- offer prepaid SIMs. No ID/registration/data needed, just pick a number and pay for it.

All of them allow roaming, for fairly steep fees.

Sunrise:
65CHF for SIM including 25CHF credit.
Domestic outgoing calls 0.69CHF/minute, incoming calls earn a credit of 0.05CHF/minute while in Switzerland.
Calling US/Europe from CH is 0.89CHF/minute.
Roaming in Europe: incoming calls 1.00CHF/minute, outgoing 2.00CHF to Europe, 4.00CHF elsewhere


Orange:
49CHF for SIM including 20CHF credit.
Domestic outgoing calls 0.90CHF/minute.
Calling US/Europe from CH is 1.00CHF/minute.
Roaming in Europe: incoming calls 1.00-1.60CHF/minute, outgoing 1.90/2.90CHF for local calls, no info provided on calls to other countries.


Swisscom:
120CHF for SIM including 80CHF credit.
Domestic outgoing calls 1.29-0.80CHF/minute (day/evening/night rates).
Calling US from CH is 1.10CHF/minute, Europe from CH 1.10-1.30.
Roaming in Europe: incoming calls 1.00-2.00CHF/minute, outgoing 2.00-3.00CHF to Europe, 5.00CHF elsewhere


Orange and Swisscom make it very hard to find this info on their websites, understandable given their roaming charges!

I recommend Sunrise to all of my visitors. Their coverage, which was lacking a few years ago, is now good.

For calling the US from Europe, using a Swiss prepaid SIM is not recommended, given the outrageous prices.


Recharging options are similar for all operators. Buying refills at ticket machines in train stations is very convenient, as one can use a mile-earning credit card at all times, and not face voice prompts in a foreign language.

All Swiss prepaid SIM's expire 12 months after last use. Keep them alive with a brief call from your home base after 11.9 months.