The "spoils of war" are as shown below. Clockwise from top left we see 9V DPDT relays (useful); the resistor packs with strange mixed values (not much good); audio transformers; 100Ω 1W resistors (useful); medium power PNP (2SB1330) and NPN (2SD2006) transistors (useful); 18nF capacitors (could be useful); and DIL 1A bridge rectifiers (useful).
For some components, like multi-pin headers, I'll sometimes use a small gas blowtorch. This will quickly melt only the solder, whereas the heat gun will often melt the plastic off the component as well before you can get it off. But you have to be careful; PCBs can emit some pretty vile gases when hot, so I usually do this on windy days when I can get good through ventilation in the garage where I play (the wind blows the vile smells away from my house and long-suffering wife). Some PCBs burn so easily (even with a hot-air gun) that they are just not worth the trouble. I'm much more selective these days, though I'll still remove resistors that are easy to get out and are at the standard 0.5 inch spacing. As a result, I have pretty well any resistor value I need with pre-formed leads, which is handy when I'm building my hobby projects.
Most of the parts I use are through-hole, and most boards nowadays are almost totally populated with surface mount devices (SMDs). I personally don't do a lot with SMD components, although they are usually easy to get off using the hot air gun on the component side of the board (which in this case I place horizontally). There are certainly lots of fairly tasty switched-mode power supply components to be had. Also, I recently purchased a bunch of Adafruit's SMD adapter boards, which make it very easy to use SMD ICs on a standard breadboard or through-hole PCB. SMD components -- especially transistors and diodes -- usually have fairly cryptic markings on them; if I can't identify them as something useful, I tend to leave them alone. A pair of SMD tweezer probes (as shown below) is really handy for quick-sorting SMD parts, and even small through-hole components.
Although my acquisitions from old PCBs (along with my natural hoarding instinct, which drives my wife nuts) mean I have just about anything I need for building up a project without going to the store or mail-order, I have to be careful when using these parts. On occasion they don't work, so a bit of time testing components that are going to be soldered in before I do so is well worth the effort.
I have a transistor tester I built when I was about 16 years old that still works fine. It comprises a 1.5V battery, a tuning meter from an old radio in series, and a 500K potentiometer, which feeds the battery to the base of the transistor. You turn the pot so that the needle of the meter gets to a certain point, corresponding to an IC of 1mA, and then read the Hfe value off the scale of the pot. You can work out the base current Ib from the pot resistance across (Vbatt - Vbe) = (1.5 - 0.6 = 0.9V) and work out the Hfe from Ic/Ib when you calibrate it. This is not real high-tech stuff, but it is incredibly useful. My Fluke 8050 desktop DMM (now around 40 years old and still going strong) had instructions in the manual to build a transistor tester attachment, which I did. I also built a capacitance meter from a couple of 555 ICs, and I have also bought a LCR meter now. What I'd really like is a 74 TTL / 4000 CMOS tester, as I get -- and use -- a lot of those ICs.
Along with my board-mounted bits, I have amassed a lot of other things like meters and switches and relays and connectors and displays and stepper motors and... I use these occasionally and, as I mentioned above, it's really handy to have them to hand if I need them, but I seem to amass more than I can ever use unless I go into production. I work on the theory that if anything is useful, I'll keep it. On the other hand, if someone wants something I've got, I'll happily give it to them if they can find a use for it. So if anyone wants anything unusual (and probably obsolete), let me know. Maybe I should start selling stuff on eBay...