Marion Zimmer Bradley's Darkover series can be read mostly standalone, with only a few books in "mini-series" within the series which work better if you've read the previous. This applies only to the ones she wrote herself, and not the posthumous co-author collaborations. This is nice, as it allows one to cherry-pick the best books, and skip the distressingly frequent lower quality ones.
Same as for Mercedes Lackey, both in and outside of Valdemar. Though for the Valdemar books, you kind of have to start with the first book of any given "set". And you may be mildly spoilered for the fates of the lead characters of any preceding "set" if they happen to show up in the one you're reading.
Steven Brust's excellent Vlad Taltos fantasies can be read in practically any order after the first book. They're mostly not written chronologically anyway, but it helps to read "Teckla" before any of the stuff set after Vlad leaves the city, just so you have an idea of what causes him to leave in the first place.
Katherine Hall Page's Faith Fairchild cozy mysteries can be read in practically any order. They're all kind of same-y anyway, or at least that's the impression I got after reading five in a row.
Most cozy mysteries are probably like that, though with some that have gradual important relationship developments over time, it's probably best not to read books too far apart in the series back to back. Some of the historical sleuth stuff, too.
I think there's a medieval series by Katherine Hall Frazier (or a name something like that) which can be read standalone as I never got any significant references to past books or emotional/character developments when I read the one of hers that I tried. And a series with Queen Elizabeth I as a sleuth, done by an author whose first name I think is Karen which was pretty much just like that, too.
I would dearly love to recommend to you my favourite Benjamin January mysteries, by Barbara Hambly, set in antebellum New Orleans from the viewpoint of a former slave trained as a surgeon who works as a musician for his living. Alas, they really do have to be read in order for the best effect, though if they turn up at all in your library, I'd say go for it anyway; they're good enough to be worth reading in any order.
And while I don't think they're likely to turn up as e-books any time soon, Elspeth Huxley (of Flame Trees of Thika fame) wrote a trio of detective novels set in a faux-Kenya with Canadian Inspector Vachell, who is notable for having what would normally be his supporting cast completely replaced for every book. No recurring characters, no mention of past cases/situations/places. At all.
Except for the bit where he was a Mountie for awhile before being put in charge of the faux-Kenyan police.
They're still pretty entertaining reads, though, allowing for the fact that they were written in the 30s (and got reprinted in the 80s/90s).