There are different types of links, search engine algorithm evaluates and ranks. Here they go,
Internal links and External links - Both links are treated differently. If the External links are bad neighborhood sites then there are chances for your site to be dropped in search engine listing. Internal links spreads link juice according to the number of times the pages are interlinked.
Relevant links and irrelevant links - If your website link to irrelevant theme site then there are possibilities for your site to rank low.
Paid links or purchased links - Google and few search engines do not encourage Paid links that helps to pass link juice and this is considered as violation of Google's webmaster guidelines. As well all Paid links are not considered as violation. There are few solutions like adding no follow attribute to the link and by redirecting the link to a page that has been blocked by robots.txt.
Anchor text HTML Links - Within the site the HTML links with Anchor text has the most value and passes good amount of link juice.
Image Links - within the site Image links with most suitable and relevant ALT attribute gets the second level value and link juice.
At this point, as far as links are concerned it plays vital role in both on-page and off-page optimization. So start planning before you go with the types of links.