By definition most of these won't be litrpg because the vast majority of those never end, as you stated. They don't really belong in this section, but you asked here, so whatever.
I've got an off-the-wall one for you that most people probably never heard of. I read the first 5 or 6 in the 90s when they came out, but apparently there are more so I can't really comment on those. I enjoyed them for quick 200'ish page reads. Briefly, 1930s setting, a reporter wakes up with no memory and discovers he's a vampire. I cannot tell you anything about them anymore other than that it is kind of a detective style, and I enjoyed them and actively looked for the new ones back in the day. Do they hold up today? No fucking clue. I should probably reread them at some point and see. Here is the first book:
Jack Fleming, ace reporter, always had a weak spot for …
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It seems like you might like monster shit. Do you like guns too? If so, Monster Hunter International by Larry Correia might be right up your alley. It has a fair amount of gun porn in it, and some OP main character stuff later, but it takes a long time to go too far off the rails. And Agent Franks is the best. It kind of ended, and had some spinoffs that I never read or forgot, but the main series mostly finishes if I remember correctly. He also has another series that is set in the 1920s and is totally unrelated, but also very good. Both have VERY similar main characters though, and I know a lot of people complained about the Gary Stu of that, but meh.
Five days after Owen Zastava Pitt pushed his insufferab…
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Jake Sullivan is a licensed Private Eye—with a seriousl…
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The Alex Verus series is about a guy that can see various future permutations in real time, so he is constantly checking futures for the best outcome and shit. I believe it is finished, although I am not sure if I ever did. I wouldn't say they were amazing, but I read at least 8 according to Goodreads, and it looks like there are 12'ish, so hopefully they were all decent.
Enter a “gorgeously realized world”* and meet a mage de…
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Those are just off the top of my head. If you need them to be litrpg, then I'm at a loss in terms of series that actually ended. Just like war, litrpg never ends!
Other dishonorable mentions that you should never, ever start unless you love crushing disappointment are Sandman Slim and Iron Druid. Both start fucking great, maybe even through 6-10 books depending upon the series, but they both turn into utter woke cuck faggot and/or gurlpower dogshit that makes me wish I had never even started them.