Most of these will be shipping just because that's what people are most interested in writing.
https://www.fanfiction.net/s/7005076/1/The-Last-Human
Finn/Marceline, from very early on in the show. A really nice read kind of on the short side, has some real cool concepts in it. Author made 2 other stories, 1 an epilogue to this one, that are also good.
https://www.fanfiction.net/s/7290683/1/A-Thousand-Summers
Another early one, very short oneshot that's made me tear up in the past. Some weird stuff in it from the fact that it's so old, but the emotion is there and strong.
https://www.fanfiction.net/s/9913771/1/Finn-Grows-Up
Another Finn/Marceline, pretty cool sci-fi/romance story. Takes a while to update so don't get too excited. One of my favorite Finn characterizations I've seen.
https://archiveofourown.org/series/33532
Very interesting Bubblegum/Marceline/Finn love triangle in the midst of human settlement and political plots. Might be my favorite AT fic, the politics are like crack to me. Bubbline is present so be warned, but this is a really good fucking story. Read in order.
https://www.fanfiction.net/s/10913273/1/Darkest-Knight
Yet another Finnceline, just usual romance with a bad guy to fight. Pretty good, don't expect an ending though.
https://www.fanfiction.net/s/9681890/1/A-Life-to-Serve
Alternate Universe with Finn and Marceline. Kind of weird and pretty long, but I still liked it.
https://www.fanfiction.net/s/10254069/1/Addiction
Same author as above, a very dark Finnceline setup where Marceline is evil as hell but I still found this story really interesting.
https://archiveofourown.org/works/300055
A really short, but sweet dreamlike story starring Bubblegum. This one is really nice.
https://www.fanfiction.net/s/12431310/1/What-Am-I-To-You Other anon posted this and has good taste. Single best Finn/PB fic ever even if it's not romantic. Real nice drama, though it can get pretty long in the tooth because they have a screaming content for like 60,000 words straight. Still high quality stuff.