On the other hand, I've gotten desoldering bulbs to work great -- enough that I've used them to desolder one entire circuit board after another, harvesting parts. They're better for older, hand-soldered analog boards and worthless for multilayer digital boards. I modified my bulb by cutting a hole in the end opposite the sucking nib and inserting a pill bottle there, making sure the hole and the bottle have a tight fit. As the bulb over-accumulates solder, I just hold it bottle-end down, shake up and down a few times, remove the bottle full of solder and dump it into my solder recycle can. I have a long allen wrench just the right size I use to periodically ream out the bore of the bulb nib.
I've used solder suckers, but you have to have the right brand and keep it maintained with silicone grease to keep things slick and sucky. They're a much bigger pain to clean.
I've used the melt and shake or the melt and tap-on-a-solid-surface method. Again, better for hand-soldered boards and worthless on multilayered ones.
Then there's the compressed air method. That one's the most dangerous to personnel and is not recommended.
I've used high-end Pace repair and rework systems. HIgh bucks to maintain and work really well. Still, for multilayer boards, especially when working on pins tied to the ground plane, you almost always have to have a second iron on the front side to help with the heat as you use the Pace sucker on the back side.
Solder braid has it's place, but don't get sucked into the "any old shield braid" is OK for the job, because it isn't. Get the stuff made for the purpose. It's good for cleaning up solder bridges, more and more common with SMT boards.
The sucking bulb mounted on the end of an iron (I believe Ungar pioneered that one in the 1960s) is probably the most worthless system there is.
Ungar also had tip kits that had shapes to match common PCB patterns: 7-pin miniature tube socket, 9-pin miniature tube socket, octal tube socket, DIP IC and a straight bar. It took a heckuva large-wattage element to handle some of those. They all stunk!
Dean