The USA has a "not so clear and defined" path of sniper and sniper rifle employment. But here is a "semi accurate" time line of sniper rifle development in the USA. Starting at WWI, the beginning of the modern era of sniping.
well we entered so late, we really didn't have a sniper program. Used M1903's with scopes.
M1903A1's with Unertl's
M1903A4 - Designated Sniper rifle
M1C's & M1D's
M1903's and M1D's again.
Some limited use of Winchester M70 target rifles
M1903's and M1D's at the beginning
Winchester M70 Target rifles
XM21 - US Army official sniper rifle
Remington 700 Varmint rifles
M40 - USMC official adoption of remington M700 with scope, etc.
M21 - US Army, Standardized
M40A1 - USMC updated M40
M24 SWS - US Army replacement for M21
M40A2 - Never officially Adopted, but tested by USMC
XM25 - Used in limited capacity by SF, SEALs and some others.
M40A3 - New replacement for M40A1's in the USMC
M82A1 - First the USMC adopted this .50 BMG, then the US Army used it "unofficially".
XM107 - Official adoption by the US Army of the USMC M82A1 improved.
Thats about it from off the top of my head, I've probably forgot one or two.... There are some additional DMR type rifles being used in Iraq right now by both USMC and US Army, but none of them are official, and a DMR is a bit different then a true sniper rifle.