Unicode Fonts

For texts in Latin script, you might want to check the free Brill or Junicode fonts that have extensive diacritical coverage. For more options see also Medieval Unicode Font Initiative, SIL Unicode Fonts or Open-source Unicode typefaces on Wikipedia.

Tamil

Recommended reading:

Font developers: Developing OpenType Fonts for Tamil Script

Built-in Windows Fonts

Starting with Windows 10, all bult-in Tamil fonts apart from Nirmala UI have been moved to an optional feature. To enable these additional fonts, go to Settings > Apps > Apps & features > Optional features > Add a feature and install Tamil Supplemental Fonts.

Font Name Basic Block L2/01-375R
Symbols
L2/03-273
SHA
L2/04-073
Zero
L2/06-184
Om̐
L2/17-069
Supplement
Availability
Nirmala UI
since Windows 8
Vijaya
since Windows 7
Latha
since Windows XP
Arial Unicode MS
Office 2000-2013

Google Noto Fonts

Google Noto is a set of free fonts from Google, aiming to support all languages with a harmonious look and feel. Installation instructions here.

Font Name Basic Block L2/01-375R
Symbols
L2/03-273
SHA
L2/04-073
Zero
L2/06-184
Om̐
L2/17-069
Supplement
Noto Sans Tamil
Noto Sans Tamil Supplement
Noto Sans Tamil UI
Noto Serif Tamil
Noto Serif Tamil Slanted