Regarding swaps, the current preferred fixings for IRS in various currencies are given below. As with all OTC instruments, you're free to use whatever you like when you agree a deal, though most banks will stick to particular fixings.
Ccy Dom Int Alt Int
AUD BBSW BBSW LIBOR
CAD CDOR
CHF LIBOR
CZK PRIBOR
DKK CIBOR
EUR EURIBOR EURIBOR LIBOR
GBP LIBOR LIBOR
HKD HIBOR ? LIBOR
HUF BUBOR
JPY TIBOR LIBOR TIBOR (LIB/TIB spreads traded)
NOK OIBOR NIBOR (OIBOR == NORIBOR)
NZD LIBOR
PLN WIBOR
RUB MOSIBOR/MOSPRIME
SEK STIBOR
USD LIBOR LIBOR EURIBOR
ZAR JIBAR LIBOR JIBAR
General fixings available via the FT: http://markets.ft.com/RESEARCH/Markets/Interest-Rates
Quick look at what's traded in London via LCH: http://www.lchclearnet.com/swaps/volumes/settlement_prices.asp
BBSW (AFMA) delayed data
CDOR (TMX)
CIBOR (NASDAQ OMX)
EURIBOR (wikipedia)
JIBAR (wikipedia)
HIBOR (Hang Seng)
LIBOR (wikipedia)
MOSIBOR/MOSPRIME (arb.ru)
PRIBOR (Czech National Bank)
STIBOR (NASDAQ OMX)
TIBOR (JBA)
WIBOR (money.pl)
BUBOR
At Freddy's suggestion, here are the overnight swap (OIS) fixings for a few currencies, along with the instruments available for curve construction:
Ccy Fixes on Instruments
USD Fed effective FedFund contracts, then OIS
EUR EONIA Meeting to meeting (ECB) and IMM-dated fwd OIS, then spot OIS
GBP SONIA Meeting to meeting (MPC) fwd OIS, then spot OIS
AUD RBA IBOC 30 day IB contracts (like FedFunds), then OIS
The following all just have spot OIS available, as far as I know:
Ccy Fix
CAD (COInS) BoC Overnight MM finance rate (I think)
CHF TOIS
DKK DKKOIS
JPY TONAR
PLN POLONIA
Depending on your role in the market and access to market data etc, the spot OIS past a year or two may be available either as quoted OIS rates or as OIS-3m basis swaps.