Yes, both guys and girls can get Chlamydia.
In men, chlamydia may cause urethritis, which can produce a discharge from the penis or pain when urinating. If not treated, it can lead to inflammation near the testes, which can cause considerable pain, and may lead to infertility.
In women, infection often starts in the cervix. Symptoms such as a vaginal discharge, burning when passing urine, lower abdominal pain, or pain during sexual intercourse may occur. If chlamydia is not treated, it may spread through the uterus to the fallopian tubes, causing salpingitis, a painful condition which may result in infertility or ectopic pregnancy (where the pregnancy develops outside the uterus. This is potentially a life threatening condition.) In some cases, infection of the whole reproductive system — pelvic inflammatory disease (PID) — can occur.
In both sexes, infection may be present in either the throat or the rectum (anus). At either of these sites there are usually no symptoms.