Alas, XHTML and CSS do not yet seem to have a means to indicate old-style figures, so in my following examples, you'll have to use your imagination at points.
In most cases unless the surrounding text is fully capitalized it seems that a number should be "lower-cased", at least so recommends The Elements of Typographic Style. So now consider an interesting corner case. While the Chicago Manual of Style disagrees, some document styles I've used have recommended that the word "figure" be capitalized. Now given this, if we were one to write "Figure One" we would naturally capitalize "one". However, most often it is recommended to refer to a figure by an Arabic numeral. So does that mean that when writing "Figure 1" the "1" should be a titling rather than old-style figure? My inclination is, yes, it should be. Alternately, if you do follow the advice of the Chicago Manual of Style and not capitalize "figure" (or equivalents) I would imagine that in "figure 1" the "1" should be an old-style figure.
So would everyone agree that one should use titling figures anywhere you could conceivable replace an Arabic numeral with a word, such that the English word for that number, and it would be capitalized?