For years I've mentally collected off-hand references I've heard about this collection of Welsh tales. In particular, it seems to come up in conversations about fantasy books, how so-and-so got detail X from The Mabinogion, or how so-and-so transferred one of the collected tales to space, or ancient Persia, or whatever. So, when it came to filling out the "classics" section of my bookshelf, this was the place I decided to start.
I'll rely on whoever wrote this fine Wikipedia article to explain the background, and focus here on my impressions.
The stories here read like a weird mixture of myth and history; it's my understanding that real people are mentioned, along with mythological figures that have parallels in Irish and other Celtic tales from pre-Anglo Saxon days. This melding of myth and history gives The Mabinogion more of a feel of a fantasy novel than, say, collections of Greek or Norse mythology. I tried to follow some of the action on a map, but geography in these tales is very fuzzy. Fantastical places (basically the same sort of faerie or sidhe stuff you see in Irish stories) give way to real-world sites and vice-versa, like these people are able to wonder into, out of, and between parallel worlds without even thinking about it. Maybe this is a story convention but I'd like to think that for these ancient Celts, the boundary between the natural and the supernatural was almost non-existent.
These tales were transmitted orally for centuries before they were ever written down, and by the time they were written down, sort of a literary strata of Anglo-Saxon influence was laid down on top of these. The latter tales in the collection all revolve around King Arthur's court, though he himself is a minor player in most of them, and not always portrayed as all that wise or kind. The collective "writer" casts King Arthur as the Roman Emperor, and seems to classify pretty much all of Europe as his domain, giving the collection an alternate history feel.
As a gamer, I'm pleased that in almost every story, gwyddbwyll is featured as a favorite pastime, and many adjectives are lavished on descriptions of the boards and pieces. In fact, there are many compound adjectives at play throughout the whole book, and my guess is that if you read them in Welsh they would have a strong rhythm, probably derived from the oral tradition. Where descriptions of land and buildings are almost nonexistent, much care is given to describing fine details of clothing, banners, and descriptions of people, which might tell us something about the priorities of those early storytellers.
A useful thing about the edition I read was a helpful guide to Welsh pronunciation. I wouldn't have known how to say the names of some heroes at all, had it not been for the guide. I mean, how would you say "Culhwch?" According to my guide, it's "Cuh-luke."
All in all, I'm left with the impression that ancient Welsh were preoccupied with wife-swapping, sending people on ridiculous errands, turning people into pigs and maggots, wandering into the Highlands of Hell (where they have the best sheep), enjoyed trapping one another by interpreting everything literally, and cutting off people's heads and breaking their backs with spears (although we see much more of this rampant decapitation in the Irish Tain, which I'm reading now).