There are physical resource implications, but nothing else.
EDIT - and that isn't really a property of multiple databases. I mean that multiple databases will share the same memory, CPU, disk (probably). If one db is getting thrashed then other queries on any db will be affected as there will be less physical resources to go round.
In SQL Server 2008 Enterprise you have the option to create resource pools and workload groups so that activitiy in one database can't monopolise memory and processor required by other databases. In Standard Edition and in earlier versions you don't have that option.