This is what I get using WRI curated data. Click to see a larger image.

For the record, the script used is:
r = SortBy[{Length[#[[2]]], #[[1]]}&/@({#, WordData[#]} & /@ DictionaryLookup[]), -First@# &]
BarChart[Transpose[r1][[1]],
ChartLabels ->
Placed[Text[Style[#, Italic, 24]] & /@ Transpose[r1][[2]], Center, Rotate[#, Pi/2] &]]
Edit
Just answering comments and other answers, here are the 76 meanings of break according to WRI.
1 Noun Flight
2 Noun Open Frame
3 Noun Dash
4 Noun Change Of Integrity
5 Noun Holdup
6 Noun Break Of Serve
7 Noun Shot
8 Noun Pause
9 Noun Modification
10 Noun Breach
11 Noun Fortuity
12 Noun Breakup
13 Noun Occurrent
14 Noun Crevice
15 Noun Hurt
16 Noun Interval
17 Verb Weaken
18 Verb Diminish
19 Verb Injure
20 Verb Fall
21 Verb Domesticate
22 Verb Change
23 Verb Turn
24 Verb Damage
25 Verb Change Integrity
26 Verb Divide
27 Verb Check
28 Verb Develop
29 Verb Break Off
30 Verb Interrupt
31 Verb Deaden
32 Verb Break Down
33 Verb Change Voice
34 Verb Go
35 Verb Lick
36 Verb Destroy
37 Verb Diphthongize
38 Verb Disrupt
39 Verb Pause
40 Verb Tell
41 Verb Get Out
42 Verb Outstrip
43 Verb Penetrate
44 Verb Become Punctured
45 Verb Detach
46 Verb Crumble
47 Verb Bust
48 Verb Disunite
49 Verb Shoot
50 Verb Modify
51 Verb Exchange
52 Verb Express Feelings
53 Verb Trip The Light Fantastic Toe
54 Verb Give Way
55 Verb Founder
56 Verb Appear
57 Verb Scatter
58 Verb Take Flight
59 Verb Get Away
60 Verb Change Direction
61 Verb Impoverish
62 Verb Designate
63 Verb Split
64 Verb Invalidate
65 Verb Break Away
66 Verb Ruin
67 Verb Disrespect
68 Verb Trespass
69 Verb Come About
70 Verb Emerge
71 Verb Violate
72 Verb Quit
73 Verb Give Up Habit
74 Verb Vary
75 Verb Finish
76 Interjection