Originally built as a terminus where all trains called on their way into London via London Bridge then after reversal went on to Charing Cross.  The chord from Borough Market Junction was added later - certainly as far as passenger trains were concerned

 
Cannon Street has a loop???

 
Avoiding loops at Cromer and Bourne End at least, while being operationally simpler, would have needed a less-centrally placed station or some trains missing that station.  Then again, not closing the line onward from Bourne End to High Wycombe would have avoided the need for a reversal and nowadays it might even be viewed as more useful than the Marlow stub.

 
Penge tunnel avoiding line, now known as the Catford loop line. Said to have been built for HM Queen Victoria, who disliked passing through Penge tunnel on the Royal Train.

 
GW&GCJR) Northolt Junction in northwest London with Ashendon Junction stations all had platformed loops

Crewe avoiding lines, officially known as the Basford Hall and Independent Lines,

On the Great Western Main Line (GWML) running between Langley and West Drayton the Up Relief Loop

More recently built are the Acton dive-under built by Crossrail, Bermondsey dive-under built by Thamelink, The Hitchin Flyover

 
Lincoln avoiding line, Bradford avoiding line?

[edit] Relics of the crossing on Bradford's Hall Lane are slow to vanish. 2025. Older images record rails across the road.

https://maps.app.goo.gl/CwL2hx2uPBBooVug6

 
Cheltenham Loop, also known as Cheltenham & Gloucester T Loop, and now known as Gloucester Avoiding Line.  Opened in 1847, closed in 1851, reopened in 1901 and continues in use.

 

Barrow-in-Furness Station - The Park South Line

Swansea - The Swansea District Lines

Two that just popped into my head

 
"On this day" reminded me of the opening 136 years ago today (1st October 1890) of the Queen Adelaide Loop at Ely, allowing train arriving there from the direction of Peterborough to carry on towards Norwich with carrying on into the station and having to reverse there. In the days of locomotive haulage that was a faff, and with unfitted freight trains a double faff.   For all the issues with multiple units raised by some members, the savings made by many of these loops melted away.

I have listed here ten historic loops and avoiders - no two the same, still existing (not sure about Queen Adelaide thiough) but some only just.

Westbury East to North
Rhubarb
Mainadee
Queen Adelaide
Reading (West to Didcot)
Foxhall
Norwich Avoider
Rose Street Curve
Laverstock
Frome avoider
Cannon Street

And here are a further 10 places where loops could have been a huge benefit - including one or two installed in my living memory.

Coombe Junction
Bourne End
Bere Alston
Cromer
Battersby
Morcambe
Georgemas
Fort William
New Holland
Bacon Curve

What have I missed?   Should any of those not count?