Usually you have to take very high doses to get toxic effects, any excess is, in the majority of cases, excreted out.
For example, it is quite easy here to get vitamin D supplements with many times the recommended dose (30mcg vs the RDA of 5mcg), I get these on prescription once in a while when my levels drop low due to winter, red hair + freckles, and staying indoors due to bad weather
The majority of vitamins are water-soluble, and so any excess is removed in urine. Fat soluble vitamins are usually where you would have a risk of toxic effects as these are more easily stored.
For the majority of people, there is no need to take multivitamins as it is fairly easy to get your required amounts, even on an "unbalanced" diet. I do take a multivitamin due to my very restricted diet, although my blood tests usually come back fine (with the exception of Vit. D mentioned above), so it is more a peace of mind thing for me, and I suspect for many people. I only do this in winter, as my diet in summer is much higher in fresh fruit and veg content.
The levels at which toxic doses occur are also very high compared to daily intake, if you take for example vitamin C, the RDA is 90mg, and the upper limit is 2000mg, some of the B-vitamins have lower ratios if I remember.
More common side effects are things like diahorrea, especially from supplements with iron.
This link has the upper limits, effects, and cases each year: Vitamin toxicity