Create a MySQL database with charset UTF-8

 Update in 2019-10-29

As mentions by @Manuel Jordan in comments, utf8mb4_0900_ai_ci is the new default in MySQL 8.0, so the following is now again a better practice:

CREATE DATABASE mydatabase CHARACTER SET utf8mb4 COLLATE utf8mb4_0900_ai_ci;

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Answer before 2019-10-29
Note: The following is now considered a better practice (see bikeman868's answer):

CREATE DATABASE mydatabase CHARACTER SET utf8mb4 COLLATE utf8mb4_unicode_ci;

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Original answer:

Try this:

CREATE DATABASE mydatabase CHARACTER SET utf8 COLLATE utf8_general_ci;

For more information, see Database Character Set and Collation in the MySQL Reference Manual.