I find inductive proofs tend to leave me hanging - I become convinced that the conclusion is true, but I still have no intuition as to why. For example, Wikipedia's proof [0] that sum of 0..n == n(n+1)/2 is convincing, but unenlightening. There are proofs which seem much more "elegant" to me, for example, pairing (1+n) == (2+n-1) == (3+n-2) ... (n/2 + (n/2 + 1)) [1], or constructing triangles [also 1].

[0] http://en.wikipedia.org/wiki/Mathematical_induction#Example

[1] http://betterexplained.com/articles/techniques-for-adding-th...