I've alway done this by 1st heating the solder with a good temperature
controlled iron, and then sucking out the majority of the solder with a
plunger-type sucker. There are special static free solder suckers. The
iron tip should be clean with a nice thin, shinny coating of solder.
Sometimes to get the heat transferred fast, you much 1st add a bit of
fresh solder (with flux core) to help conduct the heat. This is
especially true on power or ground nets were there might be a lot of
copper on the board drawing away the heat. Once most of the solder is
gone, I touch the iron tip to the wire or pin (for a through-hole IC) on
the non-component side of the board, and try to push it away from the
hole walls. Many times, especially with a 2 terminal device, it will
fall out rather easily. Even through-hole IC will usually come out
without board damage.

Lionel wrote:

Kibo informs me that "David Sewell"
stated that:


I recall servicing GEC brand tv's many years ago, and they had double-sided
print, and they were a bit of a pain. That was a cinch compared to a
motherboard!!


Yep.


What made me think of a high power iron was because of
something I read in a forum about the solder on a motherboard being of a
higher melting point than normal.


That's incorrect. The reason it seems that way is because motherboards
have huge ground & power planes on their own layers within the PCB,
which tend to act as heatsinks when you attempt to solder/desolder any
pins that connect to power or ground. Consequently, a light duty iron
will lose so much heat to the planes that the joint won't heat up enough
to melt the solder all the way through. Ideally, you need to use a
temperature-controlled iron with a heavy tip (I use a traditional,
ultra-reliable Weller TCP station myself, & strongly recommend them). If
you don't have access to a real iron like that, the next best thing is
to use a heavier standard iron - perhaps 30-40W or so - but you'll need
to be ultra careful not to damage the pads or cook the the surrounding
parts.


I had already tried an ordinary Antex
25watt iron and braid but it did not seem to be melting the solder - then
again the thing is so small my old eyes may have been deceiving me! Never
thought of cutting the cap itself. What sort of tool do you recommend and
do you mean the part of the cap as close as possible to the wire end?


The standard tool is a small pair of side-cutters, but I usually remove
electros by heating both pads with a blob of solder covering both, &
*gently* wiggling out the cap at the same time. (If a gentle touch
doesn't move the legs, the joints aren't yet hot enough - *do not* force
them, or you'll destroy the through-hole plating!)
Use whichever method you find easiest, with care, either will do the job
correctly.