is uninteresting; the only thing that's interesting about it is its transcendentality, and that's not a big deal, because almost all real numbers are transcendental. (In fact, "almost all" seems too weak here, to me, although it is technically correct in the measure-theoretic sense.)
But I think this number is interesting. Why? Because an expression that gives it can be written with a very small number of characters (bytes of TeX code, strokes of a pen, etc.) and most numbers can't be.
Of course, this means every number anyone's ever written down is interesting, by this definition -- even if it took them, say, ten thousand characters to define it. Say we work over a 100-symbol alphabet; then there are at most 10010000 or so numbers which can be defined in less than that many characters! (There are multiple definitions for the same numbers; most things one could write are just monkeys at a typewriter, and so on -- but this is an upper bound.) But this number is finite! The complement of a finite set is still "almost all" of the real numbers.
That last paragraph, I don't actually believe. But any number that can quickly be written down is "interesting" in some (weak) sense.
(By the way, "Liouville" is not pronounced "Loo-ee-vill". And I'm told that the city of Louisville in Kentucky is not pronounced this way either.)
edit, 10:22 pm: Take a look at Cam McLeman's The Ten Coolest Numbers. (The list, in reverse order, is: the golden ratio φ = 1.618..., 691, 78557, π2/6, Feigenbaum's constant δ = 4.669201..., 2, 808017424794512875886459904961710757005754368000000000, the Euler-Mascheroni constant γ = 0.577215..., the Khinchin constant K = 2.685252..., and 163.)