Emptying the messages file wont harm your apps, it could cause an error if you have a lock on the file, say you have it open in vim, while an app tries to write to it. Depending upon the app it may just sit in a "FUTEX_WAIT" status until its available or error out completely.
How big is your /var/ filesystem? This seems very odd to me that your log files are filling up this quickly. Do you have any of your apps set in a more verbose logging, for instance, is Apache or MySQL in the "debug" log mode?