If they are used properly, which isn't often, semicolons are quite useful.

From the Chicago Manual of Style

6: Punctuation
6.60: Use of the semicolon
Chapter Contents / Semicolons

In regular prose, a semicolon is most commonly used between two independent clauses not joined by a conjunction to signal a closer connection between them than a period would. (For the similar use of a colon, see 6.65.)

She spent much of her free time immersed in the ocean; no mere water-resistant watch would do.
Though a gifted writer, Miqueas has never bothered to master the semicolon; he insists that half a colon is no colon at all.
Note that many fiction authors consider semicolons to be unnatural in dialogue and may also object to their use in narrative; editors should resist adding any in such contexts without consulting the author. For the use of the semicolon in index entries, see 15.17, 15.104. For its use in parenthetical text citations, see 13.124. For its use with a second subtitle of a work, see 13.92.

6: Punctuation
6.64: Semicolons in a complex series
Chapter Contents / Semicolons

When items in a series themselves contain internal punctuation, separating the items with semicolons can aid clarity. If ambiguity seems unlikely, commas may be used instead (see 6.19). See also 6.140. Note that when a sentence continues beyond a series (as in the third example below), no additional semicolon is required.

The membership of the international commission was as follows: France, 4; Germany, 5; Great Britain, 1; Italy, 3; United States, 7.
The defendant, in an attempt to mitigate his sentence, pleaded that he had recently, on doctor's orders, gone off his medications; that his car -- which, incidentally, he had won in the late 1970s on Let's Make a Deal -- had spontaneously caught fire; and that he had not eaten for several days.
Marilynn, Sunita, and Jared, research assistants; Carlos, programming consultant; and Carol, audiovisual editor, provided support and prepared these materials for publication.
but
She decided to buy three watches: an atomic watch for travel within the United States, a solar-powered, water-resistant quartz for international travel, and an expensive self-winding model for special occasions.