Can you use integrated authentication? For example, in SQL Server 2008 R2, the following connection string accesses the local master database using Windows credentials.
Data Source=localhost;Initial Catalog=master;Trusted_Connection=true
And I would never recommend creating SQL users for an application. You are now giving direct database access to your users, who should always be using the application (unless you explicitly allow them direct access). Additionally you are restricted by what tools SQL offers you for authentication. A common problem is per-row access, your application can do the filtering pretty easily, but creating stored procedures to duplicate it is non-trivial.
To be fair though, you do need to worry about escalation of rights attacks when using a proxied account.