for another Schengen country, or vice-versa. However, New Zealand citizens may be able to stay for more than 90 days if they only visit particular Schengen countries - see for the New Zealand Government's explanation.
If you are a non-EU/EFTA national (even if you are visa-exempt, unless you are Andorran, Monégasque or San Marinese), make sure that your passport is stamped both when you enter and leave the Schengen Area. Without an entry stamp, you may be treated as an overstayer when you try to leave the Schengen Area; without an exit stamp, you may be denied entry the next time you seek to enter the Schengen Area as you may be deemed to have overstayed on your previous visit. If you cannot obtain a passport stamp, make sure that you retain documents such as boarding passes, transport tickets and ATM slips which may help to convince border inspection staff that you have stayed in the Schengen Area legally.
Note that
• while British subjects with the right of abode in the United Kingdom and British Overseas Territories citizens connected to Gibraltar are considered "United Kingdom nationals for European Union purposes" and therefore eligible for unlimited access to the Schengen Area,
• British Overseas Territories citizens without the right of abode in the United Kingdom and British subjects without the right of abode in the United Kingdom as well as British Overseas citizens and British protected persons in general do require visas.
However, all British Overseas Territories citizens except those solely connected to the Cyprus Sovereign Base Areas are eligible for British citizenship and thereafter unlimited access to the Schengen Area.
Further note that
(*) nationals of Albania, Bosnia and Herzegovina, Macedonia, Montenegro and Serbia need a biometric passport to enjoy visa-free travel,
(**) Serbian nationals with passports issued by the Serbian Coordination
