Airbrake (formerly Hoptoad) already ignores certain errors like InvalidAuthenticityToken by default (see Airbrake::Configuration::IGNORE_DEFAULT).\
To ignore additional classes of errors, put this into config/initializer/airbrake.rb:

Airbrake.configure do |config|
  config.ignore << 'ActiveRecord::IgnoreThisError'
end

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You probably also want to ignore ActionController::MethodNotAllowed and ActionController::UnknownHttpMethod exceptions.

See the github page Show archive.org snapshot for more options on how to filter certain errors.