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:
Although that page is titled "Microsoft Office 輸入法 2010", don't worry if you have a different version of Office or don't have Office at all. You'll still be able to install this. You can also ignore the omission of Vista and XP sp3: it works on those as well as Windows 7. (It does not work in Windows 8 or later.)
Click the "下載" ("Download") button:
On the next page, select the appropriate version for your system: 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 your installation isn't stopped by an 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!
If you have Office 2013, you may see a different error about missing IME64.cab or IME32.cab files.
Solution: I've extracted the main .MSI installer files for all of you, kept the old .cab files in the folder for anyone with a newer version of Office,
and deleted the rest. So, if you don't mind downloading installation files from my site, here are the 32-bit and 64-bit versions with that problem removed:
Download IME2010_zh-tw_MSI-and-cabs-only.zip (136 MB)