Wiki syntax is a line-based syntax. There is /no/ wiki markup that spans lines. It makes editing much simpler: if you make a mistake and forget to close something, it gets closed off quickly. HTML is not designed to be human-editable; wiki syntax is.
Not that that's not enough, but of course, lines (that don't continue on the next one without a *, :, etc.) are also enclosed by (unclosed! grr)
<p> tags, and you can't put a <em> in the middle of a <p> and close it after the next <p> and call it good HTML.
A couple things... I guess I don't see it as being too difficult or too complicated for users to understand that you need to enclose text you want to place emphasis on with '''. I know that stopping at newlines prevents an entire article from being emphasized, but it also prevents users from having large sections of emphasized text (without putting emphasis marks on every line). The Howto page certainly makes it look like you have to enclose your text, and in all the pages I've edited, I've never come across a page that leaves open emphasis marks.
Also, there are lots of line spanning constructs in wikitext. <pre>, <nowiki>, <tr>, <td>, etc. Now, I _know_ that (with the exception of <nowiki>) that these are HTML constructs (and not Wikitext constructs), but to the average user, they are exactly the same. So, some things span multiple lines, and some things don't. I think that is confusing.
I guess I'd like to clarify one thing. I don't want to sound pushy, or "not a team player", or somebody who is just jumping in and disrupting the good work that everybody else is doing. And you all are doing a great job, BTW. ;)
Anyways, what I want to clarify. To me, when my mind encounters '' or ''', it thinks, "Ooo! Quotation marks that make stuff bold!". My mind is used to closing quotation marks, so I guess that's why it makes the most sense for them to span multiple lines until they are closed. I'm not sure how quotes work in a lot of other languages, but I know they're closed in Japanese much the same way (but with different symbols than quotation marks).
That's not to say that stopping them at the end of a line is a bad idea - I'm sure it helps a lot to prevent new users from making a bad mistake, seeing a messed up page, and giving up.
In the end, I'm writing a new parser for Wikipedia, not for myself. If everybody thinks it should end at newlines, I can make it do that, and that will be that. :)