Buying or selling links that pass PageRank. This includes exchanging money for links, or posts that contain links; exchanging goods or services for links; or sending someone a “free” product in exchange for them writing about it and including a link
There are several other ways to "manipulate" the SERPs this way including some of them which you have identified such as - spam comments, doorway pages, forum profiles amongst others - and Google has an algorithm codenamed Penguin which, detects and penalises webmasters who attempt to manipulate the search engines in such way (although it is more complicated than this).However, Penguin is not the only way which Google identifies people being involved in these practices as they also have a place to report the links[3].
This is one of Google's Manual Actions[4] that webmasters receive, when Google believes you are not providing the user with additional value and/or are trying to manipulate the results.
They cover everything from Thin Content (mainly through Panda) to Hacked Sites to User Generated Spam to the recent Image Mismatch Penalty etc. You can see them all here: https://support.google.com/webmasters/topic/2604771?hl=en&re...
[1] https://support.google.com/webmasters/answer/35769
[2] https://support.google.com/webmasters/answer/66356
[3] https://www.google.com/webmasters/tools/paidlinks?pli=1&hl=e...
[4] https://support.google.com/webmasters/answer/2604824?hl=en