From the Boston Globe: 

Retail stores: Open at owner’s discretion.

Liquor stores: Open.

Supermarkets: Open.

Convenience stores: Open.

Taverns, bars: Open.

Banks: Open at bank’s discretion; most open.

Stock market: Open.

Municipal and state offices: Closed.

Federal offices: Open.

Libraries: Closed.

Schools: Closed.

Mail: Post offices open; regular delivery schedule.

Parking meters: Will not be in effect, but all other traffic rules apply.

From MBTA.com:

The Red, Blue, Orange, Green, and Mattapan Line will operate on its regular weekday schedule with extra service before and after the marathon. 

Copley Station will be closed all day. Customers attending the Boston Marathon will have access to the Green Line at Hynes Convention Center or Arlington Station. Customers will only be permitted to exit from the Boylston Street side of Hynes Convention Center Station. 

Commuter rail, commuter boat, and inner harbor ferry service is on a regular weekday schedule. All buses and trackless trolleys are on a Saturday schedule.

Bicycles will not be allowed on the subway. Bicycles are permitted on the commuter rail except for peak-period trips, which are identified by shading on the schedules. 

From the City of Boston:

Streets around Copley Square will close at 6 a.m., streets inside Massachusetts Avenue will close at 9 a.m. and streets outside of Massachusetts Avenue will close at 10 a.m.