Great circle distance is probably about the only thing that can be reliably measured and doesn't change regularly, though. BGP AS Path Length (or, more specifically, the number of distinct autonomous systems between the endpoints) is the next-best thing, but is both subject to frequent changes and can only be determined reliably with access to BGP-speaking routers on both ends.
Traceroute does NOT show you how many routers, networks, carriers, or geopolitical boundaries a packet traveled, as it has no visibility below IP. This, for example, only shows as one hop on a traceroute (from Newark to
www.he.net):
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7. 10gigabitethernet5-4.core1.nyc4.he.net 0.0% 15 10.5 5.6 1.6 11.0 3.6
8. 10gigabitethernet5-3.core1.lax1.he.net 0.0% 15 61.9 63.7 61.9 72.7 3.3
... but there is, almost certainly, a lot more stuff between hops 7 and 8 than there is between hops 1 and 6.
In short, it's impossible to know how many "hops" there are between two points. So, grab a piece of string and a globe.
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