Freedom of Information requests by the Press Association found officers made racist comments online and asked crime victims to become Facebook friends.
Of 828 cases in England and Wales from 2009 to February this year, 9% ended in resignation, dismissal or retirement.
The College of Policing said there was "no place... for officers who abuse the trust placed in us by the public".
About a seventh (14%) of the cases reported resulted in no further action at all. The majority of other cases were dealt with through advice being offered to the officer in question.
Cases included:A community support officer with Devon and Cornwall Police who received a final written warning after posing with weapons on Facebook A sergeant with the same force who was given a written warning after making remarks about senior officers on the site A civilian officer in central London who posted a comment online about Muslims in London failing to observe a two-minute silence Two special constables who had to resign from Northamptonshire Police after they were pictured on a website in a "compromising position" A Gwent Police officer who was given a written warning after he "inappropriately" asked a female member of the public to be his friend on Facebook during a house visit Another PC from the force who received the same punishment for using Facebook to send an "abusive" message to a member of the public A member of civilian staff in Lancashire who resigned over their "excessive and inappropriate use of the internet during working hours" - including online auction sites, internet banking and social networking The College of Policing has a code of ethics for officers, which covers conduct online
Various forces also said staff were investigated for comments deemed homophobic, racist or "religiously aggressive".
Greater Manchester Police reported the most investigations, with 88 over the period in question. West Midlands was second highest with 74, while the Metropolitan Police recorded 69.Trust abused
Chief Constable Alex Marshall, chief executive of the College of Policing, said: "People working in policing must always be mindful of the high standards that the public expect from us.
"Our code of ethics, which was launched last month, sets out the standards which everyone in the service should strive to uphold whether at work or away from work, online or offline."
He said most police officers and staff "uphold these high standards" and that social media can be a "really useful way of us talking to the people that we serve".
But he added: "There is no place in policing for officers who abuse the trust placed in us by the public."
"Everyone in policing has to remember that if you're not prepared to put it in a local newspaper with your name at the bottom, then don't say it on social media."
The college's code of ethics urges officers to "use social media responsibly and safely".
It also suggests they "ensure that nothing you publish online can reasonably be perceived by the public or your policing colleagues to be discriminatory, abusive, oppressive, harassing, bullying, victimising, offensive or otherwise incompatible with policing principles".
And it also says officers should not publish online or elsewhere, or offer for publication, any material that might undermine their own reputation or that of the policing profession.