Dave Elliott: If it was paid for then get rid. If it is natural but junk I believe Google will largely ignore them and there are better things to be doing with your time. If you don`t know then get rid of the really obvious stuff but I wouldn`t dig too deep.
Michael Martinez: If you didn`t build them they are most likely NOT "spammy links". Link spam (to a search engine) is a very specific thing: links created solely for the sake of influencing search results. Of course, that includes links built by prior site owners and/or previous SEO providers. It also includes links created for negative SEO. But most of the so-called "junk" links that people show me are NOT spammy. They`re just not links coming from the front pages of CNN and Yahoo. The vast majority of natural links look like "junk". They are not only perfectly harmless, many of them (the majority) actually help the sites they point to.
Rob Woods: depends on how much junk there is. If there is a ton of really spammy stuff I don`t mind disavowing as an insurance policy. i.e. if 50% of links are spammy and maybe (who knows?) the trigger is at 60%, disavow the worst just to make sure continued growth of spammy links or even negative SEO doesn`t push a site past that threshold. I default to better safe than sorry, but if there hasn`t been a penalty or ranking drop, err in the side of only disavowing the worst stuff.
Tim Capper: All site build up a shed load of crap, depends on the quantity. I still do a regular sweeps on some of my largest sites. It all depends if you trust Google enough to find all the crap - I never trust Google, so I do what I can to protect the site from a real or perceived threats.