A "fully manual" approach, using none of those pesky standard library functions:

def get_max_indices(vals):
    maxval = None
    index = 0
    indices = []
    while True:
        try:
            val = vals[index]
        except IndexError:
            return indices
        else:
            if maxval is None or val > maxval:
                indices = [index]
                maxval = val
            elif val == maxval:
                indices.append(index)
            index = index + 1

What it loses in brevity, it gains in... not much.

Same idea as Asterisk, but without iterating over the list twice. Bit more verbose.

count = { 'a': 120, 'b': 120, 'c': 100 }
answers = []
highest = -1

def f(x):
    global highest, answers
    if count[x] > highest:
        highest = count[x]
        answers = [x]
    elif count[x] == highest:
        answers.append(x)

map(f, count.keys())
print answers

From empirical testing, it appears that max() and min() on a list will return the first in the list that matches the max()/min() in the event of a tie:

>>> test = [(1, "a"), (1, "b"), (2, "c"), (2, "d")]
>>> max(test, key=lambda x: x[0])
(2, 'c')
>>> test = [(1, "a"), (1, "b"), (2, "d"), (2, "c")]
>>> max(test, key=lambda x: x[0])
(2, 'd')
>>> min(test, key=lambda x: x[0])
(1, 'a')
>>> test = [(1, "b"), (1, "a"), (2, "d"), (2, "c")]
>>> min(test, key=lambda x: x[0])
(1, 'b')

And Jeremy's excellent sleuthing confirms that this is indeed the case.

You could use sorting instead:

maxed = sorted(inputlist, key=lambda i: len(i), reverse=True)
allmax = list(takewhile(lambda e: len(e) == len(maxed[0]), maxed))

which takes O(n log n) time for the sort; but it's easy and short as the longest elements are all at the start for easy picking.

For a O(n) solution use a loop:

maxlist = []
maxlen = 0
for el in inputlist:
    l = len(el)
    if l > maxlen:
       maxlist = [el]
       maxlen = l
    elif l == maxlen:
       maxlist.append(el)

where maxlist is built and replaced as needed to hold only the longest elements:

>>> inputlist = 'And so we give a demo once more'.split()
>>> maxlist = []
>>> maxlen = 0
>>> for el in inputlist:
...     l = len(el)
...     if l > maxlen:
...        maxlist = [el]
...        maxlen = l
...     elif l == maxlen:
...        maxlist.append(el)
... 
>>> maxlist
['give', 'demo', 'once', 'more']