Here is a solution using awk:

awk 'NR%4 == 2 {lengths[length($0)]++} END {for (l in lengths) {print l, lengths[l]}}' file.fastq

It reads like this: every second line in every group of 4 lines (the sequence line), measure the length of the sequence and increment the array cell corresponding to that length. When all lines have been read, loop over the array to print its content. In awk, arrays and array cells are initialized when they are called for the first time, no need to initialize them before.

Another awk solution, very similar to Frédéric's:

cat reads.fastq | awk '{if(NR%4==2) print length($1)}' | sort -n | uniq -c > read_length.txt

And to quickly obtain a graph in R:

reads<-read.csv(file="read_length.txt", sep="", header=FALSE)
plot (reads$V2,reads$V1,type="l",xlab="read length",ylab="occurences",col="blue")

You can use FASTQC. It gives you all the details you need, including the quality, overrepresented sequences, enriched k-mers etc.

Another possibility, from BBMap:

readlength.sh in=reads.fq out=histogram.txt

The default is 10bp bins with a max of 80kbp, but those can be configured (run the shellscript with no arguments for details). It's very fast, and handles fastq/fasta/sam/bam; raw/gzip/bzip2.

Save it as fastq_lenght.py and run it :)

#!/usr/bin/env python
#-*- coding: UTF-8 -*-
import sys
######################################################################################
syntax = '''
------------------------------------------------------------------------------------
Usage: python fastq_lenght.py file.fastq 
result: .txt file same name as input name plus "_lenghts.txt" 
------------------------------------------------------------------------------------
'''
######################################################################################

if len(sys.argv) != 2:
    print syntax
    sys.exit()

######################################################################################

fastq_file = open(sys.argv[1], 'r')
prefix = sys.argv[1].split('.')[0]
outfile = open(prefix + '_' + 'lenghts.txt', 'w')
seq = ''
for line in fastq_file:
    line = line.rstrip('\n')
    if line.startswith('@'):
        if seq:
            outfile.write(name + '\t' + str(len(seq)) + '\n')
            seq = ""
        name = line 
    else:
        seq = line 
outfile.write(name + '\t' + str(len(seq)) + '\n')
fastq_file.close()
outfile.close()

print '\n' + '\t' + 'File: ' + prefix + '_' + 'lenghts.txt has been created...'