It's not the numbers themselves that necessarily go into the genitive singular or plural; it's the things being counted that go into the genitive even when the number itself is nominative or accusative.
Generally, as you say, numbers ending in 1 (such as 451) will be followed by a noun in the nominative singular; numbers ending in 2-4 (such as 72 or 8,075,004) will have a noun in the genitive singular, and numbers ending in 5-9 or 0 will have a noun in the genitive plural.
HOWEVER, the numbers 11-14 -- and larger numbers ending in 11-14, such as 57,912 -- are exceptions to the above; they also take the genitive plural. Thus, if you've got a jar containing 12 spiders, it's "двенадцать паука" (gen. sg. of the masculine noun паук), but if you've got 32 spiders, it's "тридцать два пауков" (gen. pl.)
In Russian, calendar years are named with "ordinal numbers" (i.e., first, second, third...), not with "cardinal numbers" (i.e., one, two, three...). In other words, they literally say "the two thousand and fourteenth year", rather than "two thousand and fourteen." And with ordinal numbers, the above rules about putting the noun into the genitive don't automatically apply -- instead, as maxmixiv explained, the noun год will go into whatever case may be required by the grammar of the sentence, and the component "fourteenth" will then be in the same case as the noun.And so for example with dates, what would the year 2011 Apply, and what case does 2014 govern?
Is 2014 written out something like: двадцать четерынадцати года?
HOWEVER, if you want to say, for example: "The ancient Roman poet Vergil died about 1,994 years ago," THEN you'd use a "cardinal number," and the rule about numbers ending in 2-4 (but NOT ending in 12-14!) comes back into play:
Древнеримский поэт Вергилий умер примерно (одну) тысячу девятьсот девяносто четыре года тому назад.
Here, the numbers "(one) thousand nine hundred ninety-four" are all in the accusative case, while "years" is in the genitive singular.