Since the criteria fits only Military rifles I own, I'll say:
.303 British - Looks cool, served for a LOOOOONG time with a great history across nations, plenty of thump, common enough for handloading to be easy and fun. Love the platform it's used in.
6.5x55 - Way ahead of its time, ballistic giant at long range, accurate in the military platform used, even my Ljungman AG-42, gets the job done with minimal recoil, proven game getter for a long, long time.
6.5x52 Carcano - Way ahead of its time for the adoption of a "small bore" round, can be very accurate, unlike many I actually like Carcano rifles, and don't think they are junk at all.
7.5x54 MAS - Accurate and hard hitting in the two rifles I have owned, a real thumper in a handy 49/56 rifle. People hate on it for being French for whatever reason... I love it and the rifles they are chambered in.
7.7x58 Arisaka - Great design/cool looking round, easy to make brass from 06, hard hitting and very accurate per my experience, Interesting history from a country not ingrained in typical firearms culture. Love of the Type-99 platform, only makes the round better in my eyes.
7.62x54R - My God, longevity in spades, short OAL, accurate with power fully the equal of 06, not fussy to reload, feeds perfectly in my SVT-40 even with its massive rim, super accurate esp in my SAKO M39. Mother Russia knocked it out of the park with this one.
7.5x55 Swiss - Damn round just LOOKS ACCURATE and cool, fantastic K-31 platform that compliment each other perhaps the best there ever was, very hard hitting esp handloaded, way, way ahead of its time, and heck it's even a .30 cal
Although I don't have a rifle chambered in 7.65x53, it has to be one of the bests... So ahead of its time, great proportions relative to performance, accurate, greatly underappreciated, came in some of the most beautiful rifles ever made.