There are a large number of different links you should avoid. This includes the types of links I mention below as well as links from websites that get the majority of their links from these types of websites.
Links from bad neighborhoods
Do not get links from websites about certain topics such as gambling, pharma or porn unless your website is about one of thee topics. You do not want to create connections between yourself and these types of websites. They might not hurt you but will provide very little value. Links from these types of websites might hurt the price if you want to sell the website in the future.
Links from directories
Links from directories have very little to no value these days. Most directories are a waste of time. Links from directories are unlikely to hurt your website but they will not provide any benefit either. There are two exceptions to this rule. Niche-directories targetting your niche might still offer some value. The same is true for a low number of high quality paid directories. Directories that manually inspect websites and only accept very high-quality websites. Examples of such directories include BOTW and JoeAnt.
Links from web 2.0 properties
Links from web 2.0 properties that have been created simply to link to your website carry no value. There are a lot of companies that offer different services that build these types of links. They are often very cheap to buy but they are not worth wasting your time on. Avoid them and get other better links instead. One high-quality link is worth thousands of these.
Please observe that this does not mean that all links from web 2.0 properties are bad. Links from old WordPress and blogger blogs with a lot of content can still be worth getting, especially if they are relevant to the topic of your website.
Comment links
Links from commenting on blogposts are worth very little and is more likely to hurt you than to help you. Avoid these types of links unless you think they can bring you traffic: Ie only build this type of links if you have something valuable to say and where your website can help the people who read the original blog post. This type of links should only be used to get traffic, not to improve your SERP.
Profile links
Do not waste your time with these types of links. They are more likely to hurt you then to help you.
Xrumer and other automated links
Avoid these types of links as the plague. They might give you a short term boost but will hurt you in the long run.
Any links that do not improve the page
You should strive only to build links that improve the page they are placed on. Links that add value to the visitor of the page the link is placed on. Links that the reader is likely to want to click on.