Yes, there are, and if you think you have symptoms of vitamin deficiency such as iron or vitamin D, then you see your doctor (not the internet) for a consultation in case you need more than a standard daily multivitamin and mineral formula (MVM). Generally if you are using a good MVM that also contains 600-1000 IU of vitamin D along with a normal diet, you would have your daily vitamins and mineral requirements met. The exception would be iron levels (and possibly calcium).
A good MVM may have a little iron but not enough to make up for a clear deficiency and therefore you would want your status assessed. A measurement of plasma ferritin and total iron-binding capacity (TBC) are used to determine iron status. There are other specialized highly specific tests for individual vitamins and minerals, but these are only necessary after you have seen your doctor for a full check up.
If you appear healthy, and you are taking a proper daily MVM, you don't need to take a blood test to find out vitamin status unless advised by your doctor. Standard blood tests offered over the internet or from other sources, unrelated to your medical history and doctor, are not valid for assessing TRUE vitamin status. Measuring vitamin status with tissue samples or blood are problematic because of vitamin instability when exposed to light, oxygen, heat, etc., during testing. Additionally, circulating blood levels only tell you what's in the blood, not what's in storage. In summary, everyone should include a daily MVM to help meet your needs, not a test to determine if you need vitamins unless your doctor prescribes it.