I hesitate to post this, because it may sound like I'm disagreeing with others, but I'm not. I decided to post my response because I think it reflects well, why there are so many cartridges: because people shoot for so many different reasons and have so many different interests. So, here's a little list from me:
.22 LR: Everyone's favorite, because it's cheap, accurate, and suited to so many different situations, like indoor shooting.
.30-'06: It's almost unpopular to like this very popular cartridge. I like it because there's such a great many bullets available in .308", and because so much research has been done with it. In other words, a lot of information is available for it and it's suitable for many situations.
.270: In my Ruger #1, it's very accurate, flat shooting, and can be used in a great many situations, all the way from varmints up to fairly large, non-dangerous game. It makes a better varmint caliber than the .30-06, in that, where the 130 gr bullet in .308 is not optimal, a 130 gr boat tail in .270 is dandy for long range, windy conditions, such as what one finds in the mountains, when rockchuck shooting.
.45-70: big bores may not be everyone's cup of tea, but what they do really well is shoot cast bullets, which is why I have kept my .45-70 reloading supplies, even after giving that gun to my older son.
7.62x54r: The Finns seem to have made this caliber quite successful in their target rifles based on the old Mosin Nagant action, keeping this round relevant into the 80s. (However, in Finland, it's known as the 7.62x53r.) Undoubtedly, messing with old Mosin Nagant actions is just as much of an exercise in futility as messing with SMLEs, when it comes to ultimate accuracy, but for some, including me, it is fun and rewarding:
TKIV 85
Finnish Army Weapons
These rifles come from a long line of 7.62x54r - Mosin Nagant development by the Finns:
Like these M39s, which are like mine.
One very nice thing about 7.62x54r right now where I'm at is the availability of low-cost surplus ammo for practice and plinking. No other high power centerfire can be shot as cheaply at this time, as you can see from this ad (which, BTW, isn't the cheapest available ammo):
Polish 7.62x54R 440rd Can 1950s Light Ball
I will admit, my M39 seems to prefer heavy ball (~ 170 gr, as opposed to ~ 145 gr), but at this price, who can gripe? There's no doubt that, if one wishes to get into the milsurp (what military surplus is called over here) bolt action shooting game, the Swiss K-31 is the way to go, especially the later ones with the ugly blond beech stock. The machine work on them is a thing of beauty, I will admit. However, there's two strikes against them in my book: First, the 7.5 mm ammo is superbly accurate for common ordinary military surplus, but it's outrageously expensive. (Reloading for milsurp shooting contests usually puts one in the next higher level of competition.) The second strike against the K-31 for me is that, even more than milsurp M98s, they are made on the "one size fits all" plan, which includes the shortest midgets in Switzerland. There are also some who prefer a nice M96 Swede in 6.5x55, but to me they are too vanilla and boring. But the M39 is often regarded as a "Jack the Giant Killer," due to its inherent accuracy. For the guy who wants to buy and shoot on a budget in this game, the M39 is a real blessing, especially to someone who wants a milsurp bolt action that has a stock proportioned for someone my size.
The 203 gr soft point Barnaul ammo in 7.62x54r is very accurate in my M39, and what I shot for competition. (The lowest level requires either milsurp or commercial ammo -- no handloads.) In fact, in my M39, this cheap-looking steel case ammo easily outshot the fancy (and expensive) Sellier & Ballot Match Boat Tail Hollow Point ammo. (At least I got some reloadable brass out of those boxes.) Also, I wouldn't hesitate to use the 203 gr Barnaul for hunting, either!
6.5x55: I have to agree, a little Swede carbine I once had was a dandy shooting little rifle.
.30 H&H: There are hotter shooting .30 Magnums -- I guess I don't much care for any of them. For one thing, the belt is superfluous on them, since there is an ample neck for them to headspace on. The taper of this one makes the belt serve a useful purpose! Why do I like it? Well, I just do. I'd love to have an old Remington 30 or 30s in .30 H&H, since most of the work to remove the ugly enfield sight and magazine belly has already been done, and the Enfield action is more than long enough and strong enough for these long cartridges (which isn't necessarily true for the M98).
.375 H&H: I also like this one for the same reason as the .30, but also because it has long seemed to me to be an ideal candidate for shooting cast bullets.
.425 Westley Richards: The big deal to this one is its ability to offer African dangerous big game capabilities in a standard length M98 action (unlike the .375 H&H, which requires lengthening and therefore weakening the M98). The use of a rebated case even made the need for opening the bolt face up unnecessary, since it's the same diameter as the 8x57/.30-'06 case rim. My interest has to do with it's potential for cast bullet shooting.
6.3x53r: This is the necked down "varmint" version of the 7.62x54r. It's pretty popular in Finland, Russia, the Baltics, etc. If chamber reamers were more available for this one in the USA, I'd be very interested in making up a nice varmint rifle on one of my Mosin Nagant actions.
Regarding the "what I don't like" category, I'd have to say, "None." There are plenty of cartridges I'm not interested in, but I can't say I've run across any I don't like.