From the monorail’s holiday service page:
On December 31. 2014, the Monorail will be open until 1:00 AM for the New Year’s Eve fireworks at the Space Needle. Due to regulations, the Monorail will carry its last passengers from Westlake Center to Seattle Center at approximately 11:15 PM. We will resume service from Seattle Center to Westlake Center once we receive the ‘ALL CLEAR’ from the Fire Marshall (estimated to be 12:20 AM) – from this point we will carry passengers until 1:00 AM.
The last southbound Link train will depart Westlake Station at 1:13 am.
The last Tacoma Link streetcars depart Tacoma Dome Station at 12:36 northbound and Theater District Station at 12:48 southbound.
A full list of New Year’s Eve and New Year’s Day service reductions can be found here.