Hello All,
Newbie here. And should make a post, because my teacher tells me, too. LOL @ Rocky.. No honestly just want to know more on these kinda tags and why this one in particular is recommended by a few sites I've been to, to be posted on a links page.
<meta name="robots" content="noindex,nofollow">.

And, should a person put these on all pages of their website, not this particular tag but others like: <meta name="robots" content="noindex,nofollow" />
<meta name="robots" content="noindex,follow" />
<meta name="robots" content="index,nofollow" />
<meta name="robots" content="index,follow" />

Also, what effect do these have in comparison or do they have the same effect:
<meta name="robots" content="index,follow">
<meta name="robots" content="all">

AFAIK Robot meta tags only work when used negatively. Thus 'index follow' is ignored and only 'no index, no follow' are recognized by robots.

Stopping robots/spiders indexing a links page may have some use if these are link farm links and it's inbound links that are important not outbound.

a robots.txt file is a sites root directory is also important...

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Paul Bilton design services ~ Sites not Sights

I agree...ditch those meta tags (there is not nearly as much importance on those anymore), and get a robots.txt file.

If you're unsure of how to set that up, just google it

Hope that helps!