My ambition to make this Anthology April, alas, didn't appear, but I did want to acknowledge the alliteration with a list of some recommended anthologies:
This Is My Funniest (Mike Resnick): I'm a sucker for humor, but what distinguishes this anthology is that the stories are chosen by what the author deems is their funniest - and it includes offerings from writers that aren't traditionally thought of as humorists. I think this anthology starts off weak, so stick with it: the stories get steadily better as the pages progress.
I, Alien (Mike Resnick): Alien encounter stories from the first-person perspective of the alien. There are a few truly moving tales in this one, and the closing piece is just delightfully clever.
Murder By Magic (Rosemary Edghill): The requirements for this anthology were that the story had to have a murder and a fantastic element, and the writers are chosen from both the fantasy camp and the mystery camp. The results are wonderful, and surprisingly, some of the worldbuilding comes from the mystery writers. If you are planning on reading Laura Resnick's novel Doppelgangster, skip her short story herein: it's the basis from which the novel was fleshed out.
Sword & Sorceress XVII (Marion Zimmer Bradley): It may take some searching to find this particular older volume, but it's probably the strongest in the series. Full review here.
The Book of Kings (Richard Gilliam, Martin H. Greenberg): A thought-provoking, imaginative anthology of kings based in both history and fantasy. Full review here.
Fantastic Companions (Julie E. Czerneda): This anthology frames itself as being about the animal companions of humans, and this isn't really accurate - but ignoring the drift from theme, this is full of entertaining, varied and surprising stories. From cats and dragons to more imaginative creatures, well worth the read. Full review here.