Which creatures don't speak Common?

There's two steps to this one.

Step one is finding the data in a format that's easy to manipulate. The base SRD documents are in .rtf format, which isn't very good for querying. Andargor's database doesn't include the languages. D20SRD.Org's Monsters section is in HTML format, which allows the use of Google but not much else (although "site:www.d20srd.org/srd/monsters/ -Common" will get you close).

In the end, I wound up using the Pathfinder dataset. There seems to be a lot of overlap in basic monsters, and I would expect there to be little difference in the languages spoken by the monsters.

Update:
user867 confirms that there has been some change to languages in Pathfinder, particularly to accommodate the addition of the "Aklo" language. For a strictly D&D 3.5 feel, use the method below to get ideas and then hand-check the candidates against the 3.5 SRD.

Step two is working with the data. I like LibreOffice's database application for this (mostly because I'm already familiar with SQL).

Download your dataset (I found getting the ODS version of the Pathfinder data to work the smoothest).

Launch Base, and choose "Connect to an existing database" (the third option in the first step of the Database Wizard). As I'm using an ODS file, I choose Spreadsheet from the list, and browse for my file.

Create a new SQL query. Like this:

Select *
From Sheet1 --This is the name of the table imported from the spreadsheet.
            --May be different depending on what type of file you imported.
            --Find it in the "Tables" section.
Where
    left(languages, 6) <> 'Common' -- Eliminate records that begin with "common"
    And Not Languages Like '% Common%' --Eliminate records containing the word
                                       --Common, preceeded by a space. To allow
                                       --for Undercommon.
    And Languages <> ''        --To be thorough about eliminating creatures with
    And Languages Is Not Null  --no languages.

Cross-check the Pathfinder results against the D&D stats, just in case the race is one of the ones that changed between versions, and you should be good to go.

I'm feeling a bit under the weather, so I haven't quite done a full step-by-step. Let me know if you get stuck, and I'll try to put more effort into that section.

A creature with int 11 or less has no bonus languages. Most creatures that commerce with "civilized" communities have common as a bonus language.

When a creature has 11 or less intelligence and is not in contact with civilization, it's safe to assume it does not speak common. Otherwise, it's pretty sure it does, unless it's a planar creature.

I would have simply gone with any creature that has < 2 INT since they cannot speak. However, I have known a lot of campaign worlds with custom continents where the "Common" language is relative only to a certain region on char-gen. Therefore even when a critter/character/whatever has the Common tongue it is not the party's dialect. Compare American English to English in the UK to Australia. There are a lot of common aspects but can be considered wholly different languages.

EDIT1: Consider specialty languages like High Elven or Druidic

EDIT2: If you would like a modern day equivilant for sub-English languages there are things like Jive and Ebonics but usually something like that is equated to a thieves cant.