Electrolysing vinegar
As @Amritansh Singhal said, $\ce{H2}$ would be produced at the cathode from the electrolysis of both the water and some from the acetic acid (main ingredient of vinegar after water) and $\ce{O2}$ would accordingly be produced at the anode.  

The question in your comment "Would it create ethane?" is where some more interesting chemistry might take place.  The short answer is "very little at the most" since in the presence of water, the cell potential will be limited by the electrolysis of water as described above.  

However, if you could obtain pure acetic acid and produce the proper cell potential, then you could see the Kolbe electrolysis reaction, which would produce ethane.  According to excerpts from this Wikipedia article":


  "The Kolbe reaction is formally a decarboxylative dimerisation of two
  carboxylic acids (or carboxylate ions)."


With respect to acetic acid specifically the above article states:  


  "The reaction mechanism involves a two-stage radical process:
  electrochemical decarboxylation gives a radical intermediate, then two
  such intermediates combine to form a covalent bond. As an example,
  electrolysis of acetic acid yields ethane and carbon dioxide:"
  $$\ce{CH3COOH → CH3COO− → CH3COO· → CH3· + CO2}$$
  followed by:
  $$\ce{2CH3· → CH3CH3}$$  


Where the latter product is ethane.