Many types of fluid have been used over the years to fill liquid-damped compasses.  The presence of fluid acts to damp the horizontal circular oscillation of a compass card and allows the card to settle on north much faster than air-damped compasses.  Liquid-damped compasses traditionally have a floating compass dial that turns instead of a moving needle supported over a fixed card - but occasionally you will see exceptions.
Compasses manufactured between circa 1904 and the late 1960s will almost certainly still contain the remains of Radium-based luminous paint.  This is an extremely highly radioactive substance and potentially very dangerous.  These compasses should not be opened by non-qualified personnel as the fluid, which will have been in contact with the Radium for many decades, will be as radioactive as the Radium itself.  If the Radium paint, dust from the paint, or fluid that has been in contact with the Radium is ingested, inhaled or enters the body through a cut or scratch on the skin then it would be wise to seek urgent medical assistance, taking the compass and parts with you, sealed in a suitable container. 
So, assuming you wish to top-up or replace old compass fluid, what should you use?  Firstly, if there are bubbles in the compass you must first fix the cause of the bubbles or lack of fluid, otherwise replaced fluid will simply escape the same way as the original fluid escaped.  If there is suspected Radium in the compass then do not do this work yourself.  Substances such as putty and silicone sealant are not recommended as they only make a terrible mess and simply do not work.  You need to find original seals, or make new seals to the exact size, shape and profile of the originals.

Compass fluids
The best fluid to use for any compass, old or new, is purified kerosene.  Purified kerosene is transparent, has low-volatility, does not generally damage painted surfaces or mother-of-pearl dials (tests should be carried out first if unsure), it is gentle on rubber and silicone gaskets and seals, and ideal for all compasses.  If your compass previously contained a different fluid then it is wise to flush out the old compass and all its internal parts several times with purified kerosene prior to the final filling.  Purified kerosene works under a massive temperature range, from around minus 40 Celsius to around 65 Celsius.  However, it is NOT SUITABLE FOR ALL COMPASSES so please take advice before using purified kerosene.

Stanley G-150 compasses are traditionally filled with Isopropyl alcohol.  This works fine, but I don't recommend it, and I always use purified kerosene when I service Stanley compasses.  Isopropyl alcohol is very volatile and will find any weakness in the seals and evaporate.  It is also less gentle on rubber and silicone seals, and can eventually break down the glue used to hold the two Tritium lights in place on the dial and underneath the dial.  Isopropyl alcohol is recommended only for G-150 compasses, but if purified kerosene is available then it is a better choice.  Also kerosene has a higher density and thus provides improved damping in comparison to isopropyl alcohol.
If your compass bowl is painted white inside then do not use isopropyl alcohol as it will almost certainly damage the paint.  Also, if your compass has white paint inside the bowl, NEVER let the paint dry out, especially when working on it. 
Remember that compasses are normally filled under vacuum.  This is not possible for the home user, so it is good practice to fill your compass in cool conditions, and to let it stand for 12 hours to let bubbles form, then release the bubble(s) and do a final top-up before final reassembly.

De-gassing compass fluid
Whatever compass fluid you use, unless it is de-gassed bubbles will soon appear in your newly re-filled compass. All fluids contained dissolved air, which eventually works its way back out of solution, forming bubbles. To de-gas your fluid, whether it’s isopropyl alcohol, purified kerosene, water, or any other fluid, you need to place it in a vacuum chamber for a period of time until it stops bubbling, and then it is de-gassed and ready to use.

There are many other fluids that could be used, such as tap water if the compass is very old and not likely to be used in the cold.  Water is a perfectly valid damping fluid, but freezes near zero Celsius, which is the only reason other fluids are used.  In the past a certain amount of glycerine was added to the water to prevent freezing.  The Sestrel Radiant compass by Henry Hughes and older models by SIRS Ltd used 90% water with 10% alcohol added to act as antifreeze.  I have heard of people using thinners, turpentine, turpentine substitute and various other fluids, but this is not a satisfactory or recommended practice.  One person I spoke to once said they used gin to "commercially" service liquid prismatic compasses, and I believe that they are still using it to this day.  Not very professional!
Many people ask me where they can obtain purified kerosene.  The most available form of purified kerosene is transparent, colourless lamp oil, usually available from any hardware store.  Isopropyl alcohol can be obtained from most pharmacies, but make sure you get 99.9% purity.
Whether you choose to use kerosene or alcohol, make sure that the gaskets, o-rings and seals you use are compatible with the chosen fluid, or the fluid will quickly destroy the seals.