.
If the anime girl is a leading lady in a series geared toward guys, then they're usually 'strong'. The average anime girl is anything but. Usually the damsel in distress type or fodder for fanservice and awkward adolescent situations. The best ones are the ones who start out normal or insecure and grow to become strong, rather than those who start out as a badass and don't really change. Escaflowne, 12 Kingdoms and I'd even go as far back as Gunbuster are some good examples of normalish girls who become strong.
As far as anime goes, there are a fair share of 'strong' women. It's almost a sort of prerequisite now for action shows, that there must be at least one woman who can at least match the main character--if they're not the main character themselves. However, I don't want every girl to be
Yoko or Revy or Mireille. It's fine now and then, but if they're not unique enough I lose interest.