Count instances of each unique integer in a vector in 1 line of code?

Any alternative probably will not be faster. Your loop already does only one pass through the array. Julia loops are fast, and there is no speed advantage to vectorized code, as there is in other languages.

Have a look at Julia's implementation of the hist function. This is taken directly from the Julia Standard Library:

function hist(v::AbstractVector, edg::AbstractVector)
    n = length(edg)-1
    h = zeros(Int, n)
    for x in v
        i = searchsortedfirst(edg, x)-1
        if 1 <= i <= n
            h[i] += 1
        end
    end
    edg,h
end

The "edg" parameter contains the edges of the bins. If we remove that feature, we get exactly the function you wrote.

EDIT hist has not been available in Julia Base since v0.5.0

There are a bunch of counting functions included in the StatsBase.jl package. Your tally function is equivalent to counts(zd, 1:K).

There are also methods for counting unique elements of types other than integer, too, such as countmap, which returns a dictionary mapping unique values to their number of occurrences.

I haven't tested the performance, but using the hist function should work:

hist(zd,0.5:K+0.5)[2]

gives:

5-element Array{Int64,1}: 1 4 1 0 0

or, if the zeros are unimportant, just use

hist(zd)[2]
3-element Array{Int64,1}:
 1
 4
 1

Here http://statsbasejl.readthedocs.org/en/latest/counts.html#countmap

countmap(x[, wv])
Return a dictionary that maps distinct values in x to their counts (or total weights).