I\'ve a simple application, say it has some classes and an \"extra\" one that handles database requests. Currently i\'m creating the database object everytime the app is use
You got some great answers already, with the majority concentrating on the aspect of injecting dependencies (which is a good thing), and only creating objects on demand.
The other aspect is the more important one: Do not put code that does any heavy work into your constructors. In case of a database object, this means: Do not connect to the database inside the constructor.
Why is this more important? Because not creating a database object because the using object also gets not created is no real optimization if the using object gets always created, but does not always run queries.
Creating an object in PHP is reasonable fast. The class code usually is available in the opcode cache, so it only triggers a call to the autoloader and then allocates some bytes in memory for the objects' properties. The constructor will run after that. If the only thing it does is copying the constructor parameters to local property variables, this is even optimized by PHP with "copy-on-write" references. So there is no real benefit if this object does not get created in the first place, if you cannot avoid it. If you can: even better.