Adding links is extremely useful for people who actually want to lookup the references.
DOI serve both as a link and as an identifier, so adding it is a good idea in general. (A similar thing holds for arXivID.)
Both for DOI and arXivID it should be visible as doi:1234/56781
and arXiv:1401.9999
, with an underlying link so it is clickable.
With other links, I consider them only if both DOI and arXivID are absent. It may be less stable, but still it is better than nothing.
If you are really concerned with the visual appeal, you can make the title (or journal reference) clickable without spelling out the complete link. But personally I think that for references usability is more important than visuals (at least, it is what I do for my PhD thesis).
To get you some taste, it looks more or less as (the citation style is temporary, just look at the style of links):
Another approach (from a paper) would be to hide link addresses as in:
See also: