Learn Russian: Сегодня никто не видел медведей.

The dictionary form is медведь, which is a masculine noun ending in a soft sign (-ь). For nouns ending in -ь, the Genitive plural ending is -ей. Because bears are animate (living beings), their Accusative plural form matches their Genitive plural form, making it медведей when they are the object of the sentence.

The sentence literally translates to nobody didn't see. Is this double negative correct in Russian?

Yes, Russian strictly requires a double negative! When you use a negative pronoun like никто (nobody), никогда (never), or ничего (nothing), you must also put не right before the verb.

Why is видел in the masculine singular form if nobody might refer to multiple people?

The word никто (nobody) is always treated as a masculine singular pronoun in Russian grammar. Even if you are talking about a group of women or a large crowd, the past tense verb that goes with никто must take the masculine singular ending (видел).

Since the verb is negative (не видел), is медведей in the Genitive case or the Accusative case?