Always check that the adhesive bandage is still sticking properly; if the edges start to lift, that's not a good sign. You'll also realize that the bandage has reached the end of the road if it's not able to contain the discharge from the wound any more, and... it itches! These are all signs that tell you only one thing: it's time to change the bandage. It's a good rule to follow, whether it's for wounds or burns. This will also go a long way to preventing the risk of infection.
Have you hurt your elbow? If the adhesive bandage is in a tricky spot like your elbow, for example, its ability to stick could be affected and it could lift more easily, allowing dirt and bacteria to get into your wound. One piece of advice? When the adhesive bandage is in an inconvenient place, change it regularly.
If you've had a minor sprain, you'll have to wrap it with specific bandages. Usually elastic bandages provide sufficient pressure to get your joints working again. Remember, though, that you'll have to change them about once a week.
OK... so unfortunately you've burned yourself! In that case, you'll have to be sure to change the dressing every day. A week after the accident, you'll be able to reduce that to changing it every 3 - 4 days until the injury is fully healed.