There's been some fascinating work around trying to determine the font used in the First Folio. Here's an excerpt from Reed Relbstein's research:
Despite an extensive analysis of its distinctive sorts, few Folio scholars (including Hinman) have examined the origins and characteristics of the font itself, and the limited information available in the literature to date is more a result of generalization than of detailed scrutiny. I measured the dimensions of the text font in a copy of the First Folio at the Beinecke Rare Book & Manuscript Library, Yale University, New Haven, Conn., finding twenty lines of type to measure 82.7 mm. Visual and historical evidence have led me to suggest that the font is the second pica roman of the Huguenot punchcutter Pierre Haultin (as described by H.D.L. Vervliet in The Palaeotypography of the French Renaissance), cast for Jaggard’s use probably around 1603 or 1608 by an unknown typefounder who likely inherited the matrices from Pierre’s nephew Jerome Haultin. The font was old and in poor condition when it was used to print the Folio, which supports the view that Jaggard and his pressmen did not see the Folio as an unusually important book. If the results of this research are to be accepted, they will correct two particularly enduring statements made about the font by Horace Hart in 1902: The font appears to be of French origin, not Dutch, and it was not commissioned specifically for the printing of the Folio but rather had been in use for fifteen or twenty years by 1623.
And here are some font options that have been discussed:
And the Illinois Shakespeare Festival created a free font that's similar to the FF font:
A free version of Fell Type (by Inigno Marini), which looks pretty good:
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