As we strive to make our prayers more meaningful, we should remember that “in nothing doth man offend God, or against none is his wrath kindled, save those who confess not his hand in all things, and obey not his commandments” (D&C 59:21). Let me recommend that periodically you and I offer a prayer in which we only give thanks and express gratitude. Ask for nothing; simply let our souls rejoice and strive to communicate appreciation with all the energy of our hearts.
Elder David A. Bednar, "Pray Always", General Conference, October 2008
In this season of recognizing blessings and giving thanks, and especially as I try focus my thoughts to what I have been given, I thought this concept that Elder Bednar suggests is right in line.

Though I've tried to express only gratitude and appreciation before in my prayers to Heavenly Father, asking for nothing, I haven't done so in a long while. I should make it a regular occurrence in my prayers.
I find it a bit difficult to not ask for anything though; either for myself or a loved one, or others. As if Heavenly Father would withhold blessings for someone else because I didn't ask for them.
Heavenly Father's knows what we need, what I need before I ever ask for it. So, just showing gratitude shows Him that I'm less selfish and more grateful, therefore... He is more likely to bless me without me even asking explicitly for something. So, in a way, I am asking for blessings by showing a bit more Christlike behavior but without verbally asking.