"Class" is singular so "class has", at least in US English. May not be in UK.

As Ed says, 'Our class always has..' is the only correct form in US English. In British English, however, either form is correct. We are a bit more flexible in GB.E, and use either single or plural grammatical forms for group nouns, depending on whether we are considering them as an single whole or a set of individuals. My preference here would be for 'Our class have..', as you are describing a set of personal experiences in this sentence.

Answer is "has".