I believe that most of you have seen the following image on your social media feeds one way or the other.
It is so full of lies and deceit that I wrote an answer for this and kept it saved so that I can paste it easily each time this box of lies appear on my screen. The following is my reply.
- False: She was third. According to the official court chronicler, Motamid Khan (as recorded in his Iqbal Namah-e-Jahangiri), the relationship with his other wives “had nothing more than the status of marriage.”[1,2,3]
- False: Wow seriously? Shah Jahan, was betrothed to Arjumand Banu Begum when she was 14! (1607 AD) She never had a husband before that. They married 5 years later (1612 AD) 
- True: I do not see the point here.
- False: He went into secluded mourning for a year! It was their daughter, Jahanara Begum that took the father out of his room. All his his hair had turned white, his back was bent, and his face was worn when he came back. (He was 39 years old when she died) 
But there are more facts.
- Mumtaz Mahal is not her real name her name was Arjumand Banu Begum.  The name ” Mumtaz Mahal ” was the pet name given to her by the emperor (Translation: “the most excellent of the palace” or literally “the light of the palace”) 
- He was planing to build a similar one for himself and build a “golden” bridge between them. [7,8]
- Their son, Jahangir staged a coup, imprisoned his father and took the throne. Shah Jahan lived rest of his life imprisoned in the Agra Fort. Looking at Taj mahal through his window. 
- After his death he was buried next to Mumtaz Mahal.
So I do not know how you see this, but to me it seems like he loved her very much.
 Koch, Ebba. The Complete Taj Mahal: And the Riverfront Gardens of Agra (Hardback) (First ed.). Thames & Hudson Ltd. pp. 288 pages. ISBN 0-500-34209-1, page 18.
 Qazwini. fol. 233a translated by Begley and Desai (1984), page 14
 Bloom, J. and Blair, S. (1994). “The Art and Architecture of Islam: 1250-1800”. New Haven and London: Yale University Press
 pg 300, The Mughal Throne by Abraham Eraly
Koch, Ebba. The Complete Taj Mahal: And the Riverfront Gardens of Agra (Hardback) (First ed.). Thames & Hudson Ltd. pp. 288 pages. ISBN 0-500-34209-1, page 20.
 Abu Fazl ‘Allami, Áín i Akbarí (The online link ishttp://persian.packhum.org/persian/main… but I could not find the exact page)
 Taj–Mahal documentary,Discovery Channel.
 Chandra, Satish (2005). Medieval India: From Sultanat to the Mughals 2. Har-Anand Publications. p. 272. ISBN 9788124110669. Retrieved 29 September 2012.
 Gascoigne, Bamber (1971). The Great Mughals. New York:Harper&Row. p. 243.