Are there days that are haram to fast other than Eid days?

Yes, the following are haram according to the consensus, or prohibitively disliked according to Imam Hanafi:

• The voluntary fasting of a woman without her husband’s permission 
• Fasting on the Day of Doubt (Yaum-ul-Shak) – the 30th day of Sha’ban if people doubt whether it is the beginning of Ramadan; however, scholars have agreed that it is permissible and not disliked if that day coincides with a day that a person usually offers voluntary fasts (ex: on a Monday or Thursday)
• Fasting for a woman who is menstruating or experiencing post-childbirth bleeding (nifaas)
• Fasting the second half of Sha’ban, which includes the Day of Doubt, though it becomes permissible if it is the habit of a person to voluntarily fast Mondays and Thursdays
• Fasting for one who fears a decline in his health through his fast