As of now (Winter 17 Release), Salesforce user cannot create their own bookmark of records they need to pay attention for - this is not about bookmark on Chatter feed / post, but bookmark on records.
Here an idea posted in IdeaExchange, as of now only have 360 points.
But, rather then wait Salesforce to built this, if you are Salesforce developer, or have Salesforce developer, they can built a simple script for this purpose with help of custom objects. However, if you do not have developer ready, there is a paid app in AppExchange called My Favorites.
Type: AppExchange (Managed Package)
Paid/Free: paid USD 60 / user / year
Blog last update: 13 November 2016