D&D Sphinx Lore Summary
She Loves A Good Story
The original D&D sphinx is what would eventually be called the "gynosphinx." From the outset, they are noted as lovers of riddles and stories, and this remains a throughline to the modern incarnation.
Ambivalent Allies
Originally, the gynosphinx enjoyed the taste of human blood, though this predatory nature was de-emphasized after its initial appearance. Gynosphinxes became potential allies, though it was on the PC's to earn this information, through offering treasures of their own (treasures inclusive of stories, poetry, and riddles). The sphinx, of course, could still be a threat if betrayed - they were Neutral, after all.
Divination Masters
When the gynosphinx appeared in 1e, they came with the ability to cast some powerful divination magic. This was likely one of their main appeals as allies - the revealing of powerful information that the party needed.
Divine Guardians & Testers of Mortals
Sphinxes in general in D&D are associated with the protection of divine sites. Some tales tell of how they are a blend of angel and celestial lion, created by the gods to pose magical tests of intelligence, courage, and martial skill to those who would enter the sacred lands they protect.
Boy Trouble
The gynosphinx has no less than three garbage boyfriends, each one a special and unique kind of garbage. The first and least garbage boyfriend is the androsphinx, who is a good person (chaotic good), but is jealous of the intelligence of the gynosphinxes, and is judgy of their neutral alignment. Gynosphinxes are noted as pursuing androsphinxes, who must be cajoled into breeding. The next bad is the criosphinx (with a goat head), which the gynosphinxes find revolting, and which seem biologically incapable of accepting no for an answer. They're pushy and greedy. The worst is the criosphinx (with a hawk head), which is noted as outright evil.
Also Appearing In This Game...
There's been a trend of adding at least one kind of sphinx in each edition.
1e gave us the luposphinx from Dragon magazine - evil, with magical howls. They are kind of interesting in their associations - gnolls and xvarts (!).
2e gave us the dracosphinx from the Forgotten Realms - also evil, with fire breath and a cunning love of brutal philosophies. They're noted as "not really sphinxes"...somehow? It also gave us the astrosphinx, which is a cool name and a cool design. They are malevolent sphinxes with bat wings and a (nearly) fleshless skull for a head. They are insane, and ask riddles without answers ("What is the speed of blue? How loud is down?"), which is a neat schtick for a sphinx.
3e gave us canisphinxes (jackal-headed, evil, with magical roars like an androsphinx) and the saurosphinx (who are neutral, use weapons, and, though weak, are fond of knowledge). It also gave us the loquasphinxes, who know truenames.
4e gave us sphinx mysteries, which are less a different type and more a different combat niche, with another attempt at making the riddle something that applies in combat.