The times when it's sometimes useful to not have strictures:

• Perl one-liners. That is perl -e'...'. If your code is literally one line, then the rigour that strictures enforce is unlikely to benefit you much and will just force you to type more.
• When you want to use symbolic references. But in these cases, you can just do no strict 'refs'; in a small scope, like a do {...} block.

Other than that, use strict everywhere. use warnings is often useful too, but use strict is vital.