Of course, you can reuse the fonts you bought for/with your windows-applications in Linux. But there are also some other possibilities:

• Linux Libertine - An alternative to “Times New Roman”, published under the GPL.

• Gentium - An alternative to “Times New Roman”, published under the SIL Open Font License

• Luc Devroye's site - Page with many links to sites with free fonts.

These fonts support so called smartfont technologies, like the automated generation of ligatures or language-specific variants of some characters. See the english Wikipedia entry on OpenType for details. If you want to see pictures, they can be found in the german Wikipedia article. I have not tried it myself, but OpenOffice.org 2.0.1 should support OpenType fonts.

• Charis - An alternative to “Bitstream Charter”, published under the SIL Open Font License

• Doulos - An alternative to “Times New Roman”, published under the SIL Open Font License