Yes and no. Spell-checkers in word-processing programs are great tools, and they can help you catch many mistakes. But be careful of too much reliance on them.
Spell-checkers won't catch words that are spelled correctly but are the wrong word. They're/their/there
Its/it's
Effect/affect
Spell-checkers may not catch plurals that should be singulars and singulars that should be plurals.
Spell-checkers may not catch misused or missing apostrophes. Or they may signal that correct apostrophes are wrong.
Spell-checkers often get hyphens wrong.
Spell-checkers may not always give you the preferred spelling of a word.
Spell-checkers often don't recognize personal and place names.
By all means use your spell-checker -- just remember that after spell-checking, you still have work to do to ensure your spelling and punctuation are correct!