Be sure you have a multi-tool with all the sizes of wrenches that you need for your bike, at least for some major parts like stem, seat post (collar and clamp for saddle), cleats, etc. If you need an 8mm allen wrench for your pedals only, you will probably be ok without it, since that is an odd size for many multi-tools. You don't need a chain breaker and extra links if you don't know how to use it.

Take tire levers (plastic, not metal) and spare tubes. Have a pump and/or CO2. If you have deep rims, take a valve extender. While you should carry 1 or 2 tubes that have the right length stem for your wheels, if you need to borrow a tube, it's good to have the valve extender on hand, even though they don't tend to work very well as a permanent fix.