UTF-8 is prepared for world domination, Latin1 isn't.
If you're trying to store non-Latin characters like Chinese, Japanese, Hebrew, Russian, etc using Latin1 encoding, then they will end up as mojibake. You may find the introductory text of this article useful (and even more if you know a bit Java).
Note that full 4-byte UTF-8 support was only introduced in MySQL 5.5. Before that version, it only goes up to 3 bytes per character, not 4 bytes per character. So, it supported only the BMP plane and not e.g. the Emoji plane. If you want full 4-byte UTF-8 support, upgrade MySQL to at least 5.5 or go for another RDBMS like PostgreSQL. In MySQL 5.5+ it's called utf8mb4.