I know that many other fruits (with normal flowers - e.g., peaches or plums) can be self pollinating.

But how can a fig tree be self pollinating?!?
Recently, I noticed some (foreign) ebay fig plant/cutting listings claiming so.
(fig seeds are also listed! - are they really viable?).

I think that self-pollination is a rather misleading fig-term and
'self-pollinating' is NOT-equal to 'no-caprification-needed'.

Common figs are self-pollinating in the sense that they produce fruit WITHOUT pollination, where "self-pollinating" means they don't need a separate tree to provide the pollen. You don't need a male and a female tree.

The seeds of a fig tree, to be viable, need to be pollinated, as I understand it. I am consistently told that if my figs have viable seeds, they must have been pollinated. Don't know where the pollen comes from in my neighborhood, but it doesn't come from my trees.

The viable seeds can produce "common" type figs if they were pollinated by a persistent caprifig (or so I am told).

I agree self-pollinating is not the same an no-caprification-needed".

True self-pollination requires "perfect" flowers which possess both male and female parts, or both male and female flowers on the same tree (such as pecan). Some plants have perfect flowers or both male and female on the same plant, but still require pollen from a different tree to set fruit. Some apples are this way - they need to different varieties, not just 2 trees, to set fruit.

I read an article on African fig wasps that traveled over 100 miles to pollinate fig trees.  No idea if European fig wasps can do that.

Looking at Enderub figs (edible caprifig) this year when collecting pollen from them--I noticed lots of pollen distributed inside the fig and the seeds were very hard, like caprified fig seeds. Will these figs pollinate themselves? I neglected to save the seeds, although I know where I threw the figs in case any seedlings sprout.

Just like Jon said, it is not self pollinating, since they really don't pollinate themselves and don't get viable seeds. 
Scott, 
a certain crop of a capri fig can get viable seeds, but in areas where the wasps survive, these seeds are eaten by the wasps. 

This gets more interesting.

Jon,
There is also apomixis, or the formation of viable seeds without fertilization (pollination). I remember reading that apomixis is at least moderately common in figs and that it was one of the traits Condit was interested in. A common fig that produced a lot of apomictic seeds would have been a boon to the dried fig industry as it would mean you would get the caprified flavor without the wasp.

But then apomixis is definitely not self pollination. It results in a clone of the mother tree, not a recombination of genes.