For some strange reason I'll be typing and suddenly the font will change, a new pop-up window opens or I'm suddenly entering text into a field on a completely different application.
 
I'm thinking my Logitech keyboard is spewing out signals and they have nothing to do with what I'm doing. Before I go buy a new one, I'm wondering if anyone else has seen this type of behaviour. I have run Malwarebytes and checked my system for viruses and there's nothing showing up.

I haven't seen that but before you spend the money on a new keyboard, I would test it in a new USB port, or if it's wireless plug the transmitter in a new USB port.

If it's wireless, also check the batteries...

Yup, as keys wear, springs give and crap gets under them so they may trigger. My left CTRL key (also Logitech) has a different spring and gets used a lot (all elongated keys have angled springs). That began sticking and was the weirdest bug to chase because CTRL-commands are all over. I suddenly realized what it was when I spun the mouse wheel... CTRL-mouse wheel is a Windows zoom command. That key even looks "semi-depressed."

Not sure if this is your case as well, but ctrl, alt, shift all have assignments, so may be able to find it.

If that is the case, most keys do simply pry out, but depending if you can identify it and want to fuss with it, a new keyboard may be simpler.

Lint on the optical eye of a mouse is another fun bug to chase (and may also be the issue).

ampfixer
For some strange reason I'll be typing and suddenly the font will change, a new pop-up window opens or I'm suddenly entering text into a field on a completely different application.
 

that could be a signal transmission issue between the two hemispheres of your CPU, which is sometimes fixed by cooling the system with a somewhat bitter coolant of low ethanol content

If you buy a new one go with Microsoft.  Not a fan of Logisuck even those most of what I have is Logisuck.  In my perfect world it's hard to beat the Ps/2 port.  They haven't ditch those yet.  I HATE Bluetooth wireless.  I use a cable that came from a wireless adaptor so my Logitech keyboard would not put me in easily killed mode for games.
I still like their older stuff. One of them though would eat batteries. 
 

Thanks for the ideas. My system runs cool all the time, so I'm not thinking it's anything more than a flaky keyboard. It's wireless and back-lit so it looks good and it's functional. But it's flimsy and doesn't have any visible means to take it apart and check the keybed. That's likely an indicator of where this is headed.
 
I may switch back to my MS ergonomic. I can't remember the last time I had a keyboard that didn't use USB.

Once my keyboard would add characters when typing fast with certain keys. It was the same characters every time. Haven't had that happen in a while so never did figure out why. Could be a harmless prank worm. My old XP laptop had one... the CD door would open regularly for no reason.