There are currently many stylish options for transporting guitars. For touring and long distance travel, most musicians prefer the added protection of a hard case. Traditionally these have been made of wood, which can be a rather heavy, but in recent years fibreglass and plastic cases have become common, much to the relief of touring musicians.
For daily use many players prefer to use a lightweight gig bag. These tend to be fairly inexpensive and usually provide ample protection. Some even have space for two guitars or basses.
If you intend to fly with your instrument, it's definitely worth checking with the airline whether your instrument will be as hand luggage in a gig bag; if they insist on putting it in the hold, a flight case (or at least a traditional hard case) is essential.