> ok varð gengit lengra en hann ætlaði
> "and he went further than he intended"
> (Yngvars saga víðförla)
>
>...
>
> In English to say "he HAPPENED to go further than he
> intended" would add a sense that it was pure chance and not intended
> by anyone or caused by anything in particular: it didn´t necessarily
> *have* to happen that way, it just did. Does `verða' ever convey a
> similar sense

That is, to me, exactly what it means.

The wording emphasizes that the act is not consciously
planned but just something that, well, happened. Note
that the word 'honum' is omitted.

"ok [honum] varð gengit lengra en hann ætlaði"

dat. + VERÐA + pp.

> And how about phrases like: hann lét verða farit "he went"; hann lét
> hana verða tekna "he seized her". Zoega in these examples just uses
> the English indicative, and there doesn´t seem to be any suggestion
> of chance involved.

This is a bit different. There is no dative involved.
I'd translate it as "he had her seized", though.

> Here's another idiom where `verða' doesn't seem to add any extra
> meaning: Henni varð þat fyrir at hún bítr einn þeirra til bana
> (Völsunga saga), at least not in Byock's translation: "She bit one
> of the brothers to death". The old Magnússon and Morris translation
> has: "and the first thing she did was to bite one of those brethren
> till he died." Surely no accident. On that sombre note...

Here we have the dative again. You could translate
"It happened to her that she bit one of the brothers to death"
but as you remark that may not make sense in the context :)

Perhaps the phrase doesn't carry much meaning there.
Maybe you can translate it with a meaningless English
phrase, say: "And it came to pass that she bit one of the
brothers to death".

Kveðja,
Haukur