Which is better: one database per application, or just one database?
I agree with mrdenny to have 1 database per Application. There are many good reasons to do that :


Most importantly Log :
SQL Server uses transaction log to be able to allow a point-in-time recovery in case of any disaster, provided that log backups are regularly taken when the database is online.
Full Backups : Easy to manage per application and can be prioratize based on critical to less critical application databases.  
DR situation : Easy to manage in scenarios like application crash, server down or failover scenarios. You have the flexiblity of just performing failover of 1 application or all - depending on if you want to test DR for just 1 application or all.
Performance consideration and Problem Isolation : When the application gets busy, it can easily be migrated to new server with less activity. Also, think about locking, blocking and deadlock situations where the same database is being accessed by multiple applications causing all sorts of issues for troubleshooting. It becomes easy to just concentrate on a single application performing bad when you have 1 database per application.
Capacity Planning : You can easily establish baselines to see what applications will require more disk space in the future and possibly migrate them to a new server having enough disk space.
Database Maintenance : The maintenance will be easy as you can concentrate on specific application's databases and give them priority as opposed to just one single database for all applications. The overall maintenance time can be reduced when performing checkdb, rebuild/reorg indexes, update stats, etc.


Above are just some advantages of using 1 database per application. There are more, like having different requirement of database recovery models, backup schedules, collation, etc as well.

Also, you can think of logically separating within the database using different schemas.