The 1905-O Half Dollar has a small mintage but it is only semi-scarce at best and it is actually quite plentiful in Mint State. MS63 and MS64 are the grades that a collector is most likely to encounter, but there are also some fabulous Gem and Superb examples for those that seek top quality. The Dr. Wynsen example that Akers mentioned below went through a number of hands (Dale Friend, Joseph C. Thomas, and Eugene Gardner) and it last sold as a PCGS MS67 for $16,450. The Eliasberg example sold again in 2015 as a PCGS MS68 for $56,400. The other PCGS MS68 (ex Duckor) sold for $54,050 in 2015.
As Akers noted, the 1905-O Half Dollars often suffer from a soft strike, but there are some well-struck examples that violate that rule.