There are many, many Russian last names that end in -ский and its variations. Good students will note that it looks like an adjectival ending, and in fact such names decline exactly like the adjective русский. The first name, of course, still declines just like an ordinary noun. Examples:

Although the last names in -ский are the most common adjectival last names, there are other last names that also decline like adjectives: Толстой declines like молодой; the last name Гладкий declines just like the uncapitalized adjective гладкий; and the last name Поперечный declines just like the uncapitalized adjective поперечный. There aren't very many of these adjectival names that don't end in -ский.

The fun really sets in, though, when you encounter last names that end in -ых or -их in the nominative case, which descended from old genitive plural forms. In these cases the last name itself does not decline, although the first name (and patronymic, if present) does. Examples:

Because such last names can be interpreted as masculine, feminine, or plural, not to mention they can be used in any case without a change of ending, interpreting the name in context can tricky. Thus «Я послал телеграмму Седых» could theoretically be interpreted to mean:

• I sent a telegram to [Mr.] Sedykh; or
• I sent a telegram to [Ms.] Sedykh; or
• I sent a telegram to the Sedykhs; or
• I sent [Mr.] Sedykh's telegram; or
• I sent [Ms.] Sedykh's telegram; or
• I sent the Sedykhs' telegram.

In such cases it is wisest to add either a first name and patronymic or some other more specific noun before the last name to clarify the situation: «Я послал телеграмму Константину Седых» or «Я послал телеграмму Наталье Седых» or «Я послал телеграмму семье Седых».