Q:

Lossy Sorting (Implement Dropsort)

Dropsort, designed by David Morgan-Mar, is an example of a linear-time "sorting algorithm" that produces a list that is, in fact, sorted, but contains only some of the original elements. Any element that is not at least as large as the maximum of the elements preceding it is simply removed from the list and discarded.
In this task, you will be given a list of integers as input (STDIN or function argument, you are required to support at least the range of 8-bit signed integers.) Your task is to dropsort them and then output the remaining elements in order.
You may assume that the list is non-empty.
This is code golf, so the shortest program wins.
Test Cases
Input             Output
1 2 5 4 3 7       1 2 5 7
10 -1 12          10 12
-7 -8 -5 0 -1 1   -7 -5 0 1
9 8 7 6 5         9
10 13 17 21       10 13 17 21
10 10 10 9 10     10 10 10 10

Leaderboard

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A:

APL, 9 bytes
⊢(/⍨)⊢=⌈\

This is a monadic function train with diagram:
┌─┼───┐  
⊢ ⍨ ┌─┼─┐
┌─┘ ⊢ = \
/     ┌─┘
      ⌈  

The non-train version is
{⍵/⍨⍵=⌈\⍵}

This basically checks if each element is equal to the running maximum.
Note that Martin Büttner's J solution is the same length as this and was posted first.

A:

J, 10 9 bytes
#~(=>./\)

Working version of my CJam idea (in fewer bytes). E.g.:
   f =: #~(=>./\)
   f 10 10 10 9 10
10 10 10 10
   f 1 2 5 4 3 7
1 2 5 7

Explanation
First, we get the maximum of each prefix, with:
    >./\

(Here, >. is the maximum operator, / folds that operator onto a list, and \ gets all the prefixes of the input.)
Then we compare the initial list with those maxima for equality:
  (=>./\)

And finally, we select all elements where this list of boolean results gave a 1:
#~(=>./\)

A:

Haskell, 28
foldr(\x l->x:filter(x<)l)[] 

An anonymous function. Call it like 
foldr(\x l->x:filter(x<)l)[] [-7, -8, -5, 0, -1, 1] 
[-7,-5,0,1]

Equivalent to the recursion 
f[]=[]
f(x:l)=x:filter(x<)(f l)

Translated iteratively, we iterate over the elements, and for each one we see, we remove the ones smaller than it from the remainder of the list that we're iterating over. Thanks to Antisthenes for a byte saved with (x<).

