Genealogy has always been moderately popular as a hobby, but in recent years it has become all the rage, thanks to TV programmes like the BBC's Who Do You Think You Are? which shows celebrities and public figures tracing their family trees (and often crossing continents in the process).
Now, I had always thought the word was geneology, but the BBC and various websites disabused me of this notion. But just the other day, one of the other students here mentioned that her dad was working on the family tree... and she said "geneology".
Let's have a look at the etymology of the word.
According to Etymonline, genealogy comes from the Greek "genea" (generation, descent), + "logia", (to speak about). So originally -logy was about lecturers, and over time was generalised to experts, and hence knowledge.
Unfortunately, the English-speaking brain doesn't understand declension of nouns, so it sees the first morpheme as "gene", not "genea", and expects the "alogy" bit to be a single morpheme. As most "-logy" words are "ologies" (biology, radiology, geology etc), we have generalised all -logies to -ologies. (Even though Etymonline has the suffix entry as "-logy".)
Don't believe me? Consider this famous advert from the 1980s:
If the English-speaking brain recognised the original morpheme boundary, would they have scripted it as "ology"? And would we have understood as easily? The popularity of the advert (it was a widely-used pop-culture reference for years after it stopped showing) suggests it's natural English.
Given all that, I can only conclude that the word is, to all intents and purposes "geneology", and that attempts to preserve the A are misguided.
Let English be English and let Greek be Greek.