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LaTeX doesn't support Unicode. You need XeLaTeX for that: http://i.imgur.com/Yx9x4.png (code is at http://paste.pocoo.org/show/295774/ )
It's hackish, but you can do Unicode in LaTeX with the inputenc and ucs packages. If you do: \usepackage[utf8x]{inputenc} \usepackage{ucs} then the inputenc macro package does a first pass on the document, handing off all non-ASCII characters to ucs to replace them with LaTeX commands to generate the appropriate characters, if supported. So, ö gets replaced by \"{o}, א gets replaced with \hebalef, etc. Doesn't work f…
\documentclass[12pt,ukrainian]{article}
\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[ukrainian]{babel}
\title{Вітаю, світе!}
\begin{document}
\maketitle
Вітаю, світе! Як ся маєшся?
\end{document}