important amplifier valves

The idea here isn't to list every valve ever used in an amplifier, just those that were widely used, or recognised as having particular merit.

Output triodes

PX4 - A valve with fans . Modern copies (by KR Audio) available here -
300B  (The 300B and 2A3 are American tubes AFAIK, these are still being made for US audiophiles)
2A3  (2.5V header)

Output pentodes and beam-tetrodes

6L6 see
KT66  (The KT44 is the lesser known 4V heater variant, with a different base and different application - TV)
6V6/6V6G/6V6GT Lower power version of the 6L6 (The 6F6 is a high gain variant)

Drivers and phase-splitters

MHL4 - As used in the Wireless World Quality Amplifier
6J6 - Replaced the earlier 6C5
6SN7GT - Another valves with fans Equivalents are ECC32 and B65
ECC82 - miniature (B9A) version of 6SN7  
ECC83 - as used in Mullard 5-10 and almost every push-pull guitar amplifier.
6SL7GT - Equivalent to ECC35

Small signal triodes and pentodes

The famous Mullard 5-10 (push pull) and Mullard 3-3 (single ended) designs both use the EF86 pentode as a first stage.  This valve was a miniature (B9A) version of the EF36.

EF36/EF37/EF37A (Octal)  6.3V 300mA heater so saw use in 6.3V parallel use and 300mA serial heater chains in AC/DC sets. Can be used as a triode (see the data sheet).

Although not used much in domestic equipment before the EF36 the SP41 and AC/SP3  pentodes were widely used as high gain audio amplifiers, e.g. as microphone amplifiers for the BBC.

Receiver valves

From the late 1930s until the end of the valve era in the early 1960s most AM broadcast receivers comprised a triode-hexode mixer, IF pentode and duo-diode triode. See "The Magic Three" for more details. 

Triode-hexode 6K8 equivalents ECH35, X61M.  Miniature types ECH41, ECH42, 6AJ8 (ECH81).
IF vari-mu pentode 6K7 equivalent KTW63
Duo-diode triode 6Q7