This depends primarily on whether you booked the connection flight as a single ticket, or separately.
If you booked the flights separately, missing the connection is entirely your risk.
If you booked a single ticket, it's the issuing airline's responsibility to fulfill the contract and deal with any unforeseen circumstances. In almost all cases, the airline will put you an a later plane.
In both cases, you may be entitled to compensation under regulations like EU regulation 216/2004 or the the airline conditions that replaced US Rule 240 after deregulation. Which one applies can be a tricky question. These regulatuions entitle you to some or all of the following:
- Acommodation, food and communication while you wait for a delayed flight or a missed connection.
- A cash compensation for longer delays.
- A choice of continuing the flight as soon as possible (perhaps even with a different airline), at a later time of, or having it refunded.
However, these may not be applicable to delays caused by "acts of god", i.e. unforeseeable factors outside the control of the airline, which would include the case you describe. But at least in the case of the EU regulation, the first point (accomodation, food, communication) is required always, up to and including volcano eruptions.