A non Torah-observant artist once wanted to give the [Lubavitch] Rebbe a portrait he had painted of him. However, the Rebbe noticed that the picture showed him with his fingers intertwined, and he explained to the artist in terms that he would relate to as to why we do not interlace our fingers.
"Others may make this mistake and may even say that they saw in the picture that this is something that the Lubavitcher Rebbe does," the Rebbe added. The Rebbe asked the artist to change this detail, stating that he would only accept the portrait once this was done. The artist was only too happy to fulfill the Rebbe's request, but he asked the Rebbe his opinion on the portrait in general. "It's much better than the original," was the Rebbe's reply.
I found here that the artist was Raphael Nouril. Read the thread for some more.
Edit: I think the prortrait is the first one here: http://raphaelnouril.com/portraits.aspx
The Aruch HaShulchan brings L'Halacha (OC 91:7) that in times of Za'am or raging tzorus, one should daven with his hands clasped together and his fingers interlocking. However says the Aruch HaShulchan in times of peace you should not do so because it causes Din Shamayim to be brought down on you.
The Piskei Tshuvos (95:5) brings that Arizal was makpid that you should never hold your hands in that manner and it is bad Mazal. Rav Chaim Palagi writes that one should stop his wife or children from doing this, ever, and especially in times of sickness or the Aseres Yimei Tshuva.
The Aruch HaShulchan says that although placing one hand inside the other is the best way to hold your hands by davening, each person is different and should keep his hands the way he feels comfortable, like on a Shtender or holding on to a shelf. However he says, make sure not to daven wearing gloves.