Snapshots are a good thing and improve your odds, but they do not guarantee consistency, especially with databases. You're basically operating with your fingers crossed. I've been using fssnap with ufsdump on Solaris for years. Even with fssnap, Sun's official line is that you should take a system down to single user to do backups. I've actually been bitten by this once or twice over the years.
A main advantage of snapshots is that you can reduce the time window that something has to be shut down or locked (
quiesce is the official term). You can shut down an application, or lock and flush tables, do the snapshot, bring them back online, and then backup the snapshot. So, instead of being shutdown for the entire backup, you are shutdown only for the few seconds it takes to do the snapshot.
You should still use proper procedures for databases.