A: Yes! A free download from Microsoft supports Windows 7, Vista and XP SP3, and despite its name does not require you to own Microsoft Office! 

In Windows XP you must enable East Asian languages. In Windows 7 and Vista, East Asian languages are enabled by default.
Install this update after Language Packs / MUI Packs for Windows or Office to avoid replacing this update with older IME files.
Go to this Microsoft download page:
http://www.microsoft.com/zh-tw/download/details.aspx?id=30390
Although that page is titled "Microsoft Office 輸入法 2010", don't worry if you have an earlier version of Office or don't have Office at all. You'll still be able to install this.
There are no important instructions on that page. Just click the appropriate "下戴" ("Download") button for your system version: x64 for 64-bit systems, or x86 for 32-bit systems.

After you download the file, double-click, install and you're done...unless you get an error message.
If you don't see the following error message, you can skip this section and scroll on down. For a while this was fixed, but it may have returned. If you do see this error message, read on...
The first time I clicked the installer, I got the very cryptic "You don't need this" message shown here. ---->
Someone at Microsoft keeps releasing IME update installers that look for Office on your system.
I think Office is distributed in Chinese markets with Chinese language packs containing the latest IME updates, and so if it sees Office the installer assumes you already have the update. I got them to fix this once in the Taiwan/HK IME updater, but now it's back - in both the Taiwan/HK and mainland/Singapore versions! While we try to get someone at Microsoft to fix it again, you have the following two options:
Option 1: "Painful Extraction"
I contacted Microsoft Support about this. They recommended I extract the installation files and do some editing as described on a
Microsoft user forum. 
I've already done that for you, so if you don't mind downloading the installation files from my site, here are the 32-bit and 64-bit versions with that problem removed:
Download zh-tw-IME-2010-update.zip
Option 2: "Painful Insertion (of credit card number)"
I didn't need to do that "extraction" for myself, because I owned the USD $24.95 Traditional Chinese Office Language Pack 2010, which contains the same Office 輸入法 2010 IME update, along with Chinese Proofing Tools and optional Chinese interface elements for Office. Microsoft seems to have pulled this off their website, but last time I checked this site was giving it away for free: Office Language Pack 2010 
There was still one final annoyance. When I purchased the Office 2010 Language Pack from Microsoft's website, the download contained only the 32-bit pack! The installer tried to tell me to uninstall Office and reinstall the 32-bit version. A quick telephone call to Microsoft Store support (Digital River)
remedied this problem however. They gave me the 64-bit version, and all is well.