We will be using the Copenhagen Card for train travel from Copenhagen to Hillerod, Helsingor, and Roskilde. I know that with the card there is no assigned seat. We would be going on weekdays in August. Is it necessary to purchase a seat assignment?

Don't think so. Have been on the train many times between Copenhagen and Helsingoer in August and have never had a seat reservation.

Thanks, Odin.

The trains to Hillerød are suburban trains (S-tog), the trains to Roskilde and Helsingør are regional trains. Seat assignment is not possible on these trains, it's more or less just like the subway, you just jump onto the train and take any free seat. Departures are every 20 minutes (every 10 minutes in rush hour on some lines).

On an August weekday, we caught the "S" at Norreport (station) and it was not at all crowded...quick ride to all places you mentioned. We stopped at Hummelbaek on the way back...and spent a few hours at the famed "Louisiana"mujseum(short walk from station), had lunch there and meandered around the exhibits and the beautiful grounds (with Sweden in sight). "Louisiana" is unique and well worth the stop. Read about it in your guide books.
stu

Thanks, chrismo and Stu. We won't bother with seat reservations and we'll definitely stop by the Louisiana Museum. Thanks for the tip.