What is the beeping occasionally heard in the background of ATC?
I can't identify the specific sound, but - just like in a cockpit - there are several different audible alerts in a control tower/control centre. Just to list a few:


Conflict alert, as suggested in the comments
Various other radar based safety nets (MSAW, MTCD, DUPE etc.)
Strip printer printing a strip (not an alert as such, but the sound is quite noticable)
Phone ringing (typically a tower has several different phones, possibly with different ringers)
Fault indication on a runway light/navigation aid
Change in status (on/off) of ILS equipment (localiser, glideslope, DME)
Crash alarm, when activated by the controller
Microwave/toaster timer! (at least in smaller towers without a separate kitchen or break room)
Several others, depending on the local equipment


It may be a bit startling when you hear something on the radio that sounds like some sort of alarm, but you shouldn't be worried. The sound can signify many different things and it does not necessarily indicate anything dangerous.