I’ll use whatjamacallit and thingamajig, but my favorite is thingamaboob.
Ryan, I’m always partial to “Who shot who in the what now?” for that kind of situation…
Framistan.
My wifes grandmother (who passed away several years ago in her late 90s) was a German Jew who had words and phrases for things that everybody else just kinda picked up. They were likely German, or maybe Yiddish, but nobody really knows.
Her word around here for a TV remote control was k-NIP-suh, but if you don’t know the name of something else, it works pretty universally for any item, especially a lost item (“have you seen the k’nip-suh?”). In practice, noone here seems to actually use the word for a remote anymore; it’s just come to mean something you’re looking for that you can’t find a name for.
I’ve really mulled over which I use for the past five minutes…and I can honestly say that the only thing I say is “the thing.” “Where’s the thing? You know, the thing. The thing that we have that does something.” How mundane.
Doobury?
I use dealy-bob and thingy, and like Eve have been known to ask about whosamacallit because I’m bad with names.
I have skipped straight from the OP to a reply so as not to be swayed or influenced by other replies. I spent the first 18 years of my life in Central Alabama, and the remainder of 60+ years in Middle Tennessee.
Terms I have heard and/or used for the non-specific “thing” are:
Dololly
Dohickey
Gizmo
Whatchamacallit (what you may call it)
Whodathoughtit (who’d have thought it)
Hickey
Thingamajig
Doodad
Dofunny
Gazinta (Goes into)
Gadget
Whatzit (what’s it)
Probably others mentioned above, which I’ll check now that I’ve worked my memory for all that’s available on a first search level.
Like Orange Skinner, I will often say “thing” if I can’t come up with at least a rough description. However, I’m usually pretty good at sounding like I know what I’m talking about, and will use a word like “device” or “mechanism.” As in, “I took the lock apart and lubricated the… bolt mechanism.”
But on the odd occasion I need a “whatsit” word, I will frequently employ a phrase of the form “(descriptor) jobby.” As in, “I adjusted the valve jobby,” or “I replaced the heater jobby.”
thinger
whatsis
widget
dealie
I’ve noticed a rather weird thing creeping in to replace whosamacallit, Eve. “Whatsherbutt” and “Whatshisface” although why it’s face for nameless guys and booty for nameless dolls, I have no idea.
If it’s an object it’s a dealy or a thingy. If it’s made out of paper, it’s kipple.
If it has to do with things in the kitchen, its “kitchenmajig”.
We were in a store many years ago and in front of us was an elderly lady asking for just such a device. “…well, you ADVERTISED it in your ad…”
I had to step out of line to compose myself.
Oh…I forgot: I also say ‘device’ on occasion, but pronounce it ‘dehv-ess.’ That’s usually only in conversations with Mudshark, however. Or to in public when I want people to look at me weirdly.
Its its an object I ususally use “dealy” in combination with some sort of description:
“…so I grabbed this here motorized dealy…”
“…what’s up with that box dealy over there…”
If its technology and I’m frustrated with using it:
“I can never figure out these new-fandangled gadgets!”
From Dictionary.com
This is what I have always heard a dongle was, but this was the 2nd use of the word. The most commn has to do with software.
Thing-a-ma-jig
Whats-her-face (whats-his-face)
A whatisit
I forgot “jobber-doober” but that’s only for mechanical things or computer parts. 
Also, I use “hummina huh?” and “hummina wha?” like Second Guest
Is “who the what now?” just a California thing, or is it merely a lazy person thing?
I’m an Okie who uses “thingy”. My husband often hears “Baby where’s that thingy? You know the thingy thing thingy!” Though sometimes I use hookey pooker. Nothing like finding your hookey pooker when it’s lost.
Quite obviously, we are utterly bereft of Mad Magazine aficionados around here. Otherwise, someone should have long ago mentioned the immortal,
Left handed veeblefetzer!
As in, “Where is that verschluginer left handed veeblefetzer!?!”