Hopefully you won't need any of this information, but in the event that you do...

24 hour emergency numbers
113 - Police (Polizia)
112 - Carabinieri
118 - Ambulance (Red Cross)
115 - Fire
(You can also call the Police or Carabinieri in case of fire or medical emergency.)

Lost or stolen documents
Passports
First you must file a report at a Carabinieri or Polizia station. Both have offices at Termini station. Otherwise, you can go to one of the following central police stations:

Carabinieri - Via Mentana, 6 (north of Termini) or Piazza Venezia (no number, but you can't miss it!) Polizia - Via Farini, 40 (south of Termini), Via S. Vitale, 15 (off Via Nazionale to the north), or Piazza del Collegio Romano, 3 (near Piazza Venezia).
Once you have filed a report at one of these offices, go to your embassy.

Travellers' Cheques

Remember to keep your cheques and the receipt for them SEPARATE.

Before filing the police report as above call the toll-free number given by your bank.

AmEx: 800 872 000
Thomas Cook/Mastercard: 800 872 050
Visa: 800 874 155
Lost or Stolen Credit Cards Call the appropriate toll-free number listed below, then file a police report as above.

AmEx: 06 72280371 (US cardholders: 800 874 333)
Diner's Club: 800 864 064
Mastercard: 800 870 866
Visa: 800 877 232
Insurance

In order to make any claims you must always FILE A POLICE REPORT. Then follow the procedure given by your insurance carrier.

Health care
E.C. Citizens are entitled to free health care but must show the E111 form. Australians are also entitled to free healthcare upon presentation of a valid MediCare card. Other foreign citizens are entitled to free emergency treatment at public hospitals.

Hospitals

Policlinico Umberto I The closest to Termini. Metro Line B: Policlinico.
Fatebenefratelli On Tiber Island , between the Ghetto and Trastevere. Bus 23.
Ospedale San Giacomo Via Canova, 29. Close to Via del Corso and the Spanish Steps. Metro Line A: Spagna.
George Eastman The only 24-hour dental hospital hospital. Viale Regina Elena, 287. Metro Line B: Policlinico.
San Gallicano Skin hospital. Via S. Gallicano, Trastevere. Tram 8.
Embassies can supply a list of doctors who speak English (or other languages).

Pharmacies

There are pharmacies (farmacie) all over Rome , recognizable by a green cross ouside. A few suggestions:

Corso Rinascimento, 48 (near Piazza Navona). Bus 492 or 64.
Farmacia Internazionale. Piazza Barberini. Metro Line A: Barberini.
Stazione Termini, Main Gallery. Open daily 7:30am -10pm. Metro Line A or B: Termini.
Late Night Pharmacies

All pharmacies have a list posted outside that indicates the pharmacies in the area which are open late at night. A few suggestions:
Piazza dei Cinquecento, 49-50-51. Tel. 06 4880019. Bus 78N to Termini.
Via Nazionale, 228. Tel. 06 4880754. Bus 78N to Via Nazionale.
Via Cola di Rienzo, 213. Tel. 06 3243130. Bus to Via Cola di Rienzo.