Produce the number 2014 without any numbers in your source code

Python, 52 bytes

print sum(ord(c) for c in 'Happy new year to you!')

Updated for 2015 thanks to @Frg:

print sum(ord(c) for c in 'A Happy New Year to You!')

Mouse over to see 2016 version:

print sum(ord(c) for c in 'Happy New Year to you!!!')

Try it online!

Ruby, 15

p Time.new.year

Temporary ;)

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Note that the section of the question

independently of any external variables such as the date or time or a random seed

was not edited in until long after I posted my answer...

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Jan Dvorak offers a great alternative in the comments:

Happy = Time
Happy.new.year

But it's so unenthusiastic. I prefer:

Happy = Time
class Time; alias year! year; end

Happy.new.year!

Or even:

class Have; def self.a; A.new; end; end
class A; def happy; Time; end; end
class Time; alias year! year; end

Have.a.happy.new.year!

And here's correct English punctuation:

def noop x = nil; end
alias a noop
alias happy noop
alias new noop
alias year! noop
def Have x
    p Time.new.year
end

Have a happy new year!

Okay okay, I couldn't help it:

def noop x = nil; end
eval %w[we wish you a merry christmas! christmas and a happy new].map{|x|"alias #{x} noop"}*"\n"
def year!; p Time.new.year; end

we wish you a merry christmas! we wish you a merry christmas!
we wish you a merry christmas and a happy new year!

Go, 2 bytes (UTF-16)

One unicode character (2 bytes in UTF-16, 3 bytes in UTF-8 format), output 2014 as part of an error

—

http://ideone.com/dRgKfk

can't load package: package : 
prog.go:1:1: illegal character U+2014 '—'