From Mountain Lion and beyond, launching TextEdit results in being confronted with the Document Picker. Fortunately, the old behavior can be restored by running a simple defaults write command in Terminal.
defaults write -g NSShowAppCentricOpenPanelInsteadOfUntitledFile -bool false
The post-Lion behavior can be re-enabled by running a defaults delete command in Terminal.
defaults delete -g NSShowAppCentricOpenPanelInsteadOfUntitledFile