JLD

https://github.com/JuliaLang/JLD.jl

Julia data file format package

StatsBase

https://github.com/JuliaStats/StatsBase.jl

Statistics functions – general

HypothesisTests

https://github.com/JuliaStats/HypothesisTests.jl

Statistics functions – hypothesis testing

PyPlot

https://github.com/stevengj/PyPlot.jl

Plotting package from Python

Gadfly

https://github.com/dcjones/Gadfly.jl

One of the best plotting packages out there

Clustering

https://github.com/JuliaStats/Clustering.jl

Clustering techniques

DecisionTree

https://github.com/bensadeghi/DecisionTree.jl

Decision trees and random forests

BackpropNeuralNet

https://github.com/compressed/BackpropNeuralNet.jl

Basic neural network trained using the algo of backpropagation

Graphs

https://github.com/JuliaLang/Graphs.jl

Complete graphs package

LightGraphs

https://github.com/JuliaGraphs/LightGraphs.jl

Relatively fast graph algorithms

PyCall

https://github.com/stevengj/PyCall.jl

Calling Python scripts from Julia

RCall

https://github.com/armgong/RJulia

Calling R scripts from Julia

DataFrames

https://github.com/JuliaStats/DataFrames.jl

Great package for integrating data frames in Julia

ELM

https://github.com/lepisma/ELM.jl

The go-to place for Extreme Learning Machines

Distances

https://github.com/JuliaStats/Distances.jl

Useful package for various distance related functions

GLM

https://github.com/JuliaStats/GLM.jl

Generalized Linear Model package

TSNE

http://lvdmaaten.github.io/tsne

An official package to implement the t-SNE algorithm

MultivariateStats

https://github.com/JuliaStats/MultivariateStats.jl

A great place to get PCA and other useful statistics functions

MLBase

https://github.com/JuliaStats/MLBase.jl

An excellent resource for various support functions for ML applications