As released RBR was offline only. But, as you may know "plugins" exist that provide online capabilities. I guess each online plugin has its own record system.
What most closely resembles what I think you want is the "hotlap" mode of the Hungarian plugin (Rallysimfans):
With this plugin you can select in game either regular rallies or online "hotlaps" for a certain stage (i.e. going 110% in search of the best time for a stage, unlike regular rallies, when usually other factors come into consideration when you run a stage). Select a physics model (original/NGP/NGP6) and a stage on the right panel in the link above to see its best times.
The more popular CZ plugin doesn't have this hotlap mode, but keeps records of every stage run in online rallies since the beginning of time, apparently:
http://rbr.onlineracing.cz/index.php?act=tstats&type=1&setlng=eng
In game you can't see the list, but every time you finish a stage online you are informed of what is the current absolute record, and the record for the car category (RC1 RC2 RGT RC3 RC4 RC5 WRC H/B H/A H/4 H/2 for the NGP cars). The only meaningful one is the car category one because the absolute record is always, or almost always, set with the old, overpowered, vanilla physics cars (C4 WRC 2008 and Focus WRC 2006 basically). Vanilla physics cars were classified in other categories (WRC N4 S2000 S1600 A8 A7 A6 A5 N3 H), so there is no possibility of conflict when you compare your times with the category record (maybe with the WRC category? The name is the same for both physics systems. I have to check but I think they are in fact different categories) It's worth noting that depending on the category, inside the same category there can be cars of vastly different performances. E.g. the Skoda 130Rs and the Fiat 126P in H/2.
When you are in shakedown mode in CZ plugin (i.e. offline single stage runs, where you can "hotlap" vs yourself if you want) you are presented a list of your best offline times for each stage (or offline/online indistinctly, if you enabled the "override records" option in the plugin), nicely separated by condition (dry/damp/wet) when you scroll over them. The caveat is that you are only shown the times of the cars you have
currently "installed" (you can only have 8 at the same time, as you may know). The records are not lost, they are kept in the rbrtmrec.dat, it's just that you have to swap cars if you want to see them all.
The plugin also saves the replay of every online stage you run and the last offline shakedown for every stage too, BTW (the
tm_shakedown... files). The plugin replay browser is also better than
main menu>replays, BTW2
As I said, the CZ plugin doesn't have a "hotlap" mode but I have seen rallies set up with the manifest purpose (stated in the rally name or description) of breaking the online record for a certain stage. For example,
Semetin 10 times in a row with a 90 min service area after each run. They are not usual, though.
As for other plugins (RSRBR..) I don't know, but CZ and Hungarian are the ones that keep up with the development of NGP physics, so they are the ones I would recommend (CZ is much more active. Even more so now, as it is used as the online infrastructure by RBRpro, currently the easiest way to enter the online side of RBR, IMHO)
