It sounds like you have 'Alerts' switched on.

'Tools' > 'Options' > 'General' or 'Menu icon' > 'Options' > 'Options' > 'General'

When new messages arrive: there are some options, some people prefer no message alerts and others prefer to hear a sound instead. unchecking all three will stop message alerts. click on OK

I just looked and alerts, sounds, tray icons are all unchecked.

Post a screen shot so we know what you are talking about.

It occurs to me that this problem began about the time of my last ThunderBird and/or FireFox upgrade. v. 38.3.0 and 42.0

I am having to disconnect because of impending lightening storm (Florida panhandle). Back in AM CST. Thank you for your help!

Is this a lot of messages open in tabs? Select one, right-click its tab, select "close other tabs". You'll be left with one or two tabs and these can be closed individually.

Yes, but the individual msgs pile up in my taskbar and closing the group sometimes closes Thunderbird. Until a month or so ago There would be only one tab in the taskbar, and that was for the program in general. If I was doing something else and then I'd click on that, T-Bird would re-open. Now I get a list of msgs I haven't even opened yet in the taskbar. Fortunately the pile-up does not include deleted or junked stuff.

Reply to Airmail: This is the next day. Suddenly opening a new msg deleted the tab for the last visited. My machine had been shut down during a storm. Yesterday, however, I did a restart and the problem returned with a vengeance, with email tabs all across the taskbar. Note that right now there are two tabs for the inbox. Screen cap uploaded.

The screen shot looks like you have your system setup to open mail in a New Window and you are not very good at closing those windows after reading the message. I suggest you turn on the Message Pane by pressing F8 and read your mail there. Once in a while I get a message that is easier read in a new tab in my case but most of the time I just use the message pane. In your case you are going to have to just close all those windows to clear them out.

Please use Tools from the Menu Bar for this check. If your menu bar is not showing press the alt key. From the Menu Bar select Tools-Options-Advanced-Reading and Display

What do you have for ... Open Messages in .. New Tab ...New Window ... Existing Window

Here is what I found, a surprise to me. I go back all the way to DOS 3.1 but now I feel I am in Lower Slobovia. Thanks for your help. What SHOULD be checked here? I do not recall ever using the T-Bird "advanced" feature before. BTW, I added the stuff in the screen shot to show you the multiple identities i have to use for my starving writer business, but multiple identities never presented the current problem. What should be checked here?

You check the option that you want to use. The key is Close those windows or tabs after reading a message.

I have had occasions lately where I open my non-work identity, open one of possibly ten new emails there (just one!) and find all the others piled up in my taskbar.

I am considering re-installing the program. If you think that is not a good idea, LMK.

Thunderbird opens just like you closed it. If you left 10 message open in windows when you close it they will be there the next time you launch Thunderbird. As for reinstalling, go ahead. It will keep you busy for a while but not change how Thunderbird works normally.

PS: After posting that screen shot yesterday, after viewing it I did not click OK or anything but simply backed out of the option menu without changing anything. Now the problem has seemed to have disappeared. I hope this is permanent. WLYK.

Problem solved, and methinks it was caused by a bad spot on my desktop HDD. I have heard of such things but not experienced them myself. Thank you for your help and patience. Thunderbird rules! I remember when Outlook first appeared (AKA Lookout) and then and for years afterward incompatible with my correspondents outside the USA.