Double Factor Authentication is an absolutely must have. It is between the 10 most important security measures for any application that can be reached one way or the other by public audience.
My twitter account was recently hacked and as a result my account spammed around 10 followers with around three spams each. My apologies for this incident.
I had a strong password and I usually change them every three months (a pain, I know). I even have different passwords for my different online accounts (another necessary pain). I would have saved time but more importantly I would have saved some reputation should I have looked into the Twitter privacy section because the service offers double factor authentication.
In twitter case they support the double factor authentication with SMS or the twitter app.
Double factor authentication is an inconvenient but it is better to go through that pain than getting hacked.