While I feel it's certainly worthwhile to read the masters (by which, I mean the initial works that created entire fields of mathematics by their founders), my reasoning is somewhat different then most. Reading the masters is really more for conceptual depth than actual mathematical enlightenment.
There's a myth surrounding Abel's dictum that stems from the unreadability of the masters like Guass Gauss as a measure of their nearly inhuman brilliance. This is a fallacy. The reason the masters are so difficult to read is because we are catching them with thier their pants down in the act of creation, i.e. they are groping towards the right notation and terminology, but aren't quite there yet. For example, it's pretty clear Riemann in his doctorial doctoral lecture was trying to explain the need for higher dimensional spaces that went beyond familiar three dimensional space ("multiplely "multiply extended quantities") which preserved all the familiar properties of the usual Euclidean spaces, i.e. Klienian Kleinian transformations and calculus in local neighborhoods. The problem was without either linear algebra or the fundamentals of topology, it was next to impossible to express this idea clearly and precisely. He just ends up babbling on about what's needed. But all the same, Riemann recognized what was needed even if how to express it correctly was beyond his ability.
A more recent and readily available example will clarify this further: One of my favorite books is Hassner Hassler Whitney's Geometric Integration Theory. I have friends in differential geometry who tell me it's a dinosaur, that his proof of the de Rham theorum theorem is incredibly coarse and tedious. Yes, it is--but is — but it has the advantage of being a DIRECT proof from the construction of simplexes on the boundary of an embedded manifold. I love the book because although Whitney's ideas were old fashioned, they were incredibly powerful IDEAS that allow us to tackle the subject concretely and with an amazing amount of insight. THAT'S what we get from reading the masters-thier masters — their insight and depth of understanding that allows us to see beyond the machinery into why things are defined as they are.