With this function a random integer is inserted in the e-mail address ([email protected] becomes [email protected]) and then the hash value is computed. The hash value is used to get the corresponding identicon from the Gravatar website. This approach can address also some privacy concerns.
generatePic[email_] := Module[{emailparts, randN, input, inputhash, img}, emailparts = StringSplit[email, "@"]; randN = StringJoin["+", ToString[RandomInteger[99999]], "@"]; input = emailparts[[1]] <> randN <> emailparts[[2]]; inputhash = IntegerString[Hash[ToLowerCase[input], "MD5"], 16, 32]; img = Import[ "http://www.gravatar.com/avatar/" <> inputhash <> "?s=128&d=identicon&r=PG"]; {img, input} ]
If we want to generate some identicons based on a specific e-mail address we just do this:
Grid[Table[generatePic["[email protected]"], {3}]]

Once we find an identicon we like, we just need to copy/paste the corresponding e-mail address into the e-mail field of the Stack Exchange profile.
Update for Mathematica versions before 8
It seems that older Mathematica versions include the enclosing quotes "" when it generates the hash, but there seems to be a workaround.
StringHash[string_String, type_: "MD5"] := Module[{stream, file, hash}, stream = OpenWrite[]; WriteString[stream, string]; file = Close[stream]; hash = FileHash[file, type]; DeleteFile[file]; hash]
And then:
generatePic[email_] := Module[{emailparts, randN, input, inputhash, img}, emailparts = StringSplit[email, "@"]; randN = StringJoin["+", ToString[RandomInteger[99999]], "@"]; input = emailparts[[1]] <> randN <> emailparts[[2]]; inputhash = IntegerString[StringHash[ToLowerCase[input], "MD5"], 16, 32]; img = Import[ "http://www.gravatar.com/avatar/" <> inputhash <> "?s=128&d=identicon&r=PG"]; {img, input}]