If it's retail (not from distro disk) install, then it is 90% safe to install software updates, unless there is a system version update available (i.e. from 10.6.7 to 10.6.8). System version update are less safe, even with vanilla kernel and compatible hardware, there could be some issues (not so serious mostly).
Having a legacy kernel, you should be more careful with system version updates. If you do system version update, make sure that you have the new kernel of corresponding to the newer version. Also make sure you have a backup. It would also be wise to search the forum or google for the related info, before doing a system version update. In general it is advisable (if using legacy kernel) to be patient with system version updates and wait for some time after it's out, just to make sure that others don't have any issues with it.
Again, updates for applications/system/security updates (such as in the screenshot of yours) usually are safe enough. However different hardware configurations may behave differently, so be careful.