Basically anything contra-peak on the Uckfield Line, south of East Croydon or perhaps Oxted, the occasional school run traffic excluded. Likewise anything against the regular flows at the weekend, except if there's a festival at Eridge or something.
I am reliably informed that on the first train heading down in service on the 27th, the only passenger was the onboard cleaner, and the next wasn't much better. The third only had about 10 people over the whole journey from London Bridge, and after that I think everyone stopped bothering trying to work out how much fresh air was being carried.
Though by far the most pointless were (apparently) the Oxted-Ashurst shuttles they ran on one or two Sundays during the platform extension works. Yes, having to use buses from anywhere north of Oxted and anywhere south of Ashurst, which is in the middle of nowhere, connecting with an hourly train which the CIS couldn't track under pilotman working and just showed as "Delayed", was really going to be very useful...