Yes but it depends on which B Vitamin...
Here's the complete list.
thiamin (B1):
No known toxicity from oral intake.
riboflavin (B2):
No evidence of toxicity based on limited human and animal studies
niacin (B3):
Intake of 3000 mg/day of nicotinamide and 1500 mg/day of nicotinic acid are associated with nausea, vomiting, and signs and symptoms of liver toxicity. Other effects may include glucose intolerance, and (reversible) ocular effects. Additionally, the nicotinic acid form may cause vasodilatory effects, also known as flushing, including redness of the skin, often accompanied by an itching, tingling, or mild burning sensation, which is also often accompanied by pruritus, headaches, and increased intracranial blood flow, and occasionally accompanied by pain.[9] Medical practitioners prescribe recommended doses up to 2000 mg. per day of niacin, usually in time release format, to combat arterial plaque development in cases of high lipid levels.
Large doses (Ie, greater than 1000mg) are usually only taken as a measure to lower cholesterol in place of statins or other prescribed medications.
Also, the 'slow release' or 'no flush' formulas have been known to cause liver damage if taken in large doses.
pantothenic acid (B5):
No known toxicity
pyridoxine (B6):
All effects are unconfirmed: (peripheral) sensory neuropathy [causal association with intake of vitamin B6 is likely]; dermatological lesions [causal association is unlikely]; B6 dependency in newborns [causal association is also unlikely].
biotin (B7):
No known toxicity
folic acid (B9):
Masks B12 deficiency, which can lead to permanent neurological damage
cobalamin (B12):
Acne-like rash [causality is not conclusively established].
Note: All the information presented in block quotes is from Wikipedia.