The simple answer is because we are exciting! Dogs want to be around people for a lot of reasons, but mostly because that is kind of what dogs do. Excessive following is common especially in puppies and this is called imprinting. This behavior resembles a co-dependency but for the human side of the relationship can be excessive and rather bothersome. What can you do about it? Well, there are quite a few things you can do, but the most important step is to figure out what is causing this behavior. Depending on the root cause these behaviors may fade with time, may need professional help or possibly just easily be corrected on your own.
The Root of the Behavior
Behavior like this often resembles run of the mill separation anxiety because it is separation anxiety. These symptoms are more common in small breed dogs and young pups. Dogs with separation anxiety often tear the house to pieces when the human companions are gone and this behavior is a strong indicator that anxiety is the root cause of your problem. If your dog typically does not exhibit other symptoms associated with separation anxiety then boredom may be your culprit. Your dog follows you around all day simply because they have nothing better to do. Lack of exercise can exacerbate these issues.
Improper training can lead to your dog following you around. The way we interact each day with our dogs does more to train and educate them than any formal training process you can undertake. If you pet your dog consistently as they follow you around then they likely believe they are supposed to follow you around. This cycle of unintended behavioral reinforcement is the cause of many issues dogs have in their households. In the same vein, your own desire for them to be around when they are young can move onto their older years because they are so used to being at your side at all times. If your dog is suffering from debilitating medical issues they did not have in the past, such as recent blindness or deafness, then they may wish to be with you all the time because they are scared and are relying on you for comfort and assistance with their daily needs. This is typical and if you can address the underlying medical concerns, this behavior will usually subside. If you were in the same situation, you would likely gain an additional attachment to those helping you through. It is just because they need you. This may subside a bit as they grow in comfort with their circumstances but will likely always be more then it was before.
Encouraging the Behavior
New individuals in the household or a new animal around can increase stress in your dog and they may seek your attention for relief and comfort. The best way to start in an attempt to earn some free space is to set up an area for your dog inside the home that they can call their own. This does not need to be a large area and the important bits you likely already have. A dog bed or kennel with their favorite blanket and a few toys around that they enjoy can do wonders. Having this area removed from the high traffic areas of your home will aid in their comfort. Dog owners often use the kennel for this area due to its convenience and your dog will likely love it too. Try including some relaxing music and additional exercise to the mix. Medication is likely available from your vet but this should be considered a last resort. Like any human medication aimed at anxiety and stress reduction, these medications are powerful and alter the brain chemistry of your canine. A behavioral specialist can assist you in your efforts and help you identify and address the root cause of the behavior. These actions alone can usually cure your canine friend!
Other Solutions and Considerations
If this is a learned behavior through incidental improper training then most dog trainers should be able to correct this easily and install a few commands to aid you in the future. This would typically rely on the fact they are not plagued by anxiety or stress but simply follow you around because they believe they are supposed to. Relieve boredom by making sure your dog has some toys and things around the house they can use to occupy their time and help relieve stress by making sure they are getting plenty of exercise and a well rounded diet. Changing environments, like moving to a new home or staying with someone unfamiliar, will almost always affect their stress levels to a certain degree but should subside as they get familiar with their new surroundings.