How do different methods of transmission line termination compare?
If you are talking about high speed digital and not RF signals then you can choose one of the following schemes (all assume continuous ground planes).  Keep the stub section as short as possible and you can choose a transmission line impedance that works well for your layout (Zo=50 ohms is not a requirement).

• Simple parallel termination:  In a simple parallel termination scheme, the terminating resistor (Rl) is equal to the line impedance. Place the termination resistor as close to the load as possible to be efficient -- keep the stub section as short as possible. 







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• Thevenin parallel termination:  An alternative parallel termination scheme uses a Thevenin voltage divider. The terminating resistor is split between R1 and R2, which equals the line impedance when combined--(R1||R2)=Zo. Although this scheme reduces the current drawn from the source device, it adds current drawn from the power supply because the resistors are tied between VCC and GND.







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• Active parallel termination:  An active parallel termination scheme, the terminating resistor (Rl=Zo) is tied to a bias voltage (Vbias). In this scheme, the voltage is selected so that the output drivers can draw current from the high and low-level signals. However, this scheme requires a separate voltage source that can sink and source currents to match the output transfer rates.







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• Series-RC parallel termination:  A series-RC parallel termination scheme uses a resistor and capacitor (i.e., series-RC) network as the terminating impedance. The terminating resistor (Rl) is equal to Zo. The
capacitor must be large enough to filter the constant flow of DC current.
However, if the capacitor is too large, it will delay the signal beyond the design threshold. Capacitors smaller than 100 pF diminish the effectiveness of termination. The capacitor blocks low-frequency signals while passing high-frequency signals. Therefore, the DC loading effect of Rl does not have an impact on the driver, as there is no DC path to ground.  Not all drivers can handle the dynamic current requirements for larger capacitor loads.







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• Series termination:  In a series termination scheme, the resistor matches the impedance at the signal source instead of matching the impedance at each load. The sum of Rl and the impedance of the output driver should be equal to the Zo. Because silicon IC output impedances are low, you should add a series resistor to match the signal source to the line impedance. The advantage of series termination is that it consumes little power. However, the disadvantage is that the rise time degrades due to the increased RC time constant.







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RF and microwave terminations are another animal and depend greatly on the physical 3d parameters of your design, input and output impedance, operating frequency range.  They rarely depend on resistive elements.  They are designed by reactively moving the input and output impedances into the proper 50ohm match.

However these are passive networks so both of your cases you were curious about don't really matter -- just get the matching correct (of course your components have to be sized to handle the voltage/current demands):


  low-power RF (between stages, receivers)
  
  high-power RF (transmitters)


As for 


  What are the advantages and disadvantages of each, considering:

we might want to transfer power (as to an antenna) and not information (as in a digital circuit)
the signal may be analog
the transmission line might not be ideal (discontinuities in the middle, etc.)



Antennas are passive loads so design for max power transfer, but in their operating bandwidth they will need a matching network to do this.  Analog signals are the same as RF. Just match the impedance.  Non-ideal transmission lines is too vague to answer, but any discontinuity causes a reflection and a loss of power.