Not all major search engines give prominence to inbound and outbound links. In addition, nobody knows exactly how much importance any of the search engines actually give to how sites link to each other. However, it is safe to say that there are several factors that those search engines that do take linking into account will look for.
Use of the keyword or phrase in the link
A year or two ago this was seen as being the most important factor of all. The search engines were proactively looking for links that included the word or phrase being searched for.
For example, if you had a site specializing in astronomy and other sites that linked to you used that word in their link text that would be very good, but if they didn't mention that word then the link would still be taken into account, but it wouldn't count as much in your favor, indeed it may even count slightly against you as it may cause the search engine to think that your site was about something else other than astronomy.
In the table below are some examples of good and bad text links.
Good and Bad Link Text for the keyword 'Astronomy'
Everything you want to know about Astronomy
Astronomy – The Source
A useful Astronomy Resource
Jack Brown's Astronomy Site
Jack Brown's Web site
Sky at Night
Stars at Night
All you want to know about the Heavens
It's easy to see why a search engine such as Google would give more prominence to a site that had inbound text links like those in the Good column than it would from those in the Bad column.
Proximity is becoming important, too
Until recently it was considered enough if you had the keyword or phrase in the link text, but over the past year something called proximity has become increasingly important.
With proximity the search engine is checking to see if the keyword or phrase appears anywhere near the link that is coming into your site.
Consider how the following two paragraphs might perform for the keyword diving.
Danny's Diving Excursions - At the Marina Paso you will find everything you need for your trip. There are hundreds of boats to choose from in the nearby harbor and you can hire any equipment you might need from the stores in the Marina Shopping Village.
Mike's Diving Excursions - At the Marina Paso you will find everything you need for your diving trip. There are hundreds of boats to choose from in the nearby harbor and you can hire any diving equipment you might need from the stores in the Marina Shopping Village.
The link for Mike's Diving Excursions is likely to score higher than the first as far as keyword proximity is concerned. Both paragraphs include the keyword in the link text itself, but Mike's has the added advantage of being within 13 and 32 words of additional occurrences of the keyword diving. A search engine that uses keyword proximity as a factor would consider Mike's link to be more valid that Danny's and this might just give Mike the advantage in the search engine results.
Obviously, a single link taken in isolation is unlikely to make much difference, but if there are several dozen, or even several hundred similar links then it really will start to prove a crucial factor as far as the search engine results are concerned.