See them here, a table excerpted from Jim Hamilton’s God’s Glory in Salvation through Judgment: A Biblical Theology. (That two-page PDF is available only today through Thursday.)
These prayers that appeal to God’s concern for his own glory show how the believing remnant in the old covenant responded to God’s pursuit of his own glory: they joined him in it. These OT saints adopted God’s priorities and based their prayers on what they understood to be of greatest concern to God himself–his reputation among the nations, the glory of his name, the revelation of the truth about who he is. Moses, Joshua, David, Solomon, Elijah, Hezekiah, Jeremiah, Asaph, Asa, and Jehoshaphat all petition God on the basis of his concern for his own glory.
Incidentally, there is a massively important point of application here: this is how we, too, should pray. The perspective of the biblical authors is not merely to be studied but adopted, embraced, and lived.
These prayers appealing to God’s concern for his glory are applied to a variety of situations and employ a variety of expressions, and they had to be located the old fashioned way, which is still the best way to examine a biblical theme: by reading slowly through the OT, marking them as they appeared, and then gathering them all into one place. So this chart saves you a ton of work, but actually doing this kind of work for yourself is the best way to study the Bible because it demands that you read attentively, remember what you’ve read, correlate new information with what you’ve already seen, and assimilate the results into a coherent whole.
So in this table I list every prayer in the Old Testament that appeals to God’s concern for his own glory; at least, I think I got them all! If you find one that I missed I’d love to know about it.
See also Hamilton’s explanation on the 9Marks blog.