The world is full of electronics being unceremoniously discarded. Said electronics contains power supplies. Said power supplies contain a number of magnetics, namely transformers and chokes with ferrite cores, of all sorts of sizes and shapes (well, usually E or EI, but anyway). A computer power supply will have several. A dead CFL lightbulb will usually have a pair - a toroid for the transistors and a choke for EMI suppression.
Ferrite cores tend to be expensive and difficult to source. A way to get some for free is therefore always welcomed. However, the salvaged transformers are usually potted in some sort of resin and can not be disassembled. The ferrite is also very fragile, precluding use of force bigger than small.
The Internet in its wisdom offered a couple hints. Some about soaking the transformers in solvents for hours or days, some about boiling the transformers in water for ten minutes. Usually the methods were wet and/or smelly and generally unpleasant.
An experiment was tried with the Hot Air Blower. A ferrite transformer, after removal of the sticky tape around the core, was placed in front of its exhaust nozzle and the blower was switched on to full power. The transformer was left to cook in 200 °C air until it was so hot a drop of water sizzled on the ferrite. Then the transformer was removed from the hot air stream and the core was loosened with gentle prying with a small, thin-blade screwdriver. The material that held the bloody thing together really softens when heated up above 100 °C; the core moved slightly in the bobbin and was willing to be pried out. The other half of the core was then pushed out of the bobbin by gentle steady pressure through the bobbin's hole.
The ferrite's thermal conductivity is somewhat poor, patience is therefore needed. A thermocouple probe can be used for measuring the approximate core temperature, in order to know how fast it is approaching the desired above-boiling-point value.
The ferrite is also VERY fragile. Especially smaller cores are prone to breaking when not handled with a lot of gentle and loving care. Do not attempt to force the core out when it is not showing signs of willingness; patience and more hot air will do a good job here, like when a politico rides out a government crisis. Otherwise you risk cracking the core.
Cracked cores can be glued back together with epoxy, but their magnetic properties will likely be degraded due to the additional, even if thin, gap in the core.
The work goes much easier when the entire disassembly operation is performed in the hot air stream. When the operator has the hot air source between his body and the transformer, he can hold the transformer in pliers (hold it by the bobbin, then the pliers won't be likely to crack the core) and gently tweak and pry and teases the core out of the bobbin with a flat screwdriver. Work in hot air stream prevents the transformer from cooling down while being manipulated, hardening again and eventually cracking the core; repeated reheatings are taxing for the patience and it is tempting to just use a bit more force to avoid another waiting cycle.
It is helpful to apply gentle pressure to the core from the side, first make it move inside the bobbin for a fraction of millimeter and unstick the surfaces, and only then, once the initial movement happens, become slowly and carefully lifting the core from the bobbin. Once out, push the lower part from the bobbin by applying a gentle steady pressure through the bobbin's hole to the middle of the core; this makes it less likely to crack than prying.
There are some common places where ferrite cores can be found. Modern electronics overwhelmingly uses switching power supplies; ferrites are used as cores for the transformers. A computer power supply usually yields one big transformer and sometimes a number of smaller ones. Other appliances (TVs, VCRs...) tend to operate with lower powers and have smaller cores. Generally, the size of the core is somewhat proportional to the peak power the power supply was rated for. The smaller cores are from either very small power supplies (e.g. a cellphone charger - even those now eschew the large iron-core transformers in favor for electronics), or various coupling transformers in more complex power supplies. Some chokes are also wound on salvageable ferrite cores that can be repurposed into transformers.
Then there are many various toroids out there. Some as transformers, some as chokes. These generally do not have to be subjected to thermal treatment to be disassembled; the wire can be unwound if necessary, or just cut out of. There usually is no bobbin to care about as the windings usually are located directly on the core.
A good source of tiny toroids for e.g. the Joule thief applications is in the recycle boxes in various electronics shops, hidden inside the discarded CFL bulbs. For the inside view of a random bulb check out the CFL reverse engineering page; note the larger EE-core ballast choke (which can be disassembled with the hot-air method) and the toroid-core transformer with three windings (which does not require further processing, perhaps except removal of the old windings).
The disassembly-capable cores come in two common variants, EI and EE. The former one has a bar (I) laid over the E part with longer prongs; the I part can be usually removed easily, which is paid for by the added complexity of removal of the core going through the entire depth of the bobbin. The EE variant comes as a pair of identical E-shaped cores; the first one has to be carefully pried out (and is the one most prone to crack when too much force is applied - be GENTLE), the second one can be usually just pushed out of the core by applying pressure at the center prong through the bobbin.
Beware of air gaps. Many cores have air gaps in order to soften their saturation characteristics. This may be an advantage or a disadvantage for a given planned use. Just check what is the case by assembling the core together without a bobbin. A detail that is often overlooked when handling secondhand magnetics.
Ferrite trafos, small
Heating of small transformers
Successfully disassembled transformer
Unsuccessfully disassembled choke
Big transformer from a switching power supply
Heating the big transformer, checking temperature with thermocouple
Big transformer, I part removed
Big transformer, E and I core parts removed
Disassembled small choke from a CFL lamp, E core