There are vaccination records in various formats in many countries, but you are right, they might get lost. In newer centralized systems (e.g. UK, Canada etc.) there is often a database, but if you are older or in a decentralized system, they might not be present. However, there is an international version created by the WHO that has been around since the 70s or so. It is very recognizable yellow booklet in which vaccinations are recorded and which is internationally accepted.
For many vaccines, additional vaccinations have not shown any adverse effects (and some require refreshing anyway), so in doubt and especially if at risk, it might be worthwhile to update and document new vaccinations. Also note that vaccination schedules are different for infants, children and adults, so an unvaccinated adult generally is not just given an infant dose.