Can I have an STD for years without any symptoms?

Latent Syphilis. I agree with the prior answer. Syphilis also should be mentioned. Syphilis has a primary stage with genital skin ulceration, then follows a secondary stage with more widespread skin rashes. But the following latent or tertiary stage is downright scary. It may last for years with gradual damage to may body systems, potientially causing severe neurologic damage, even death. Get tested.
Yes. Yes, many infections can do this. Hpv, or the virus that causes genital warts and ultimately cancers of the cervix, vagina, vulva, and anus can be asymptommatic for a decade or more. Hiv can have a period without signs. Gonorrhea and chlamydia are often asymptommatic. This is why people need to be tested, and not just think 'i am clean because I feel fine'. Get tested...