Is this how your downspouts currently drain? If so they should be disconnected from the overburdened sewer system and spilled onto grade in a manner that does not adversely affect your foundation and adjoining properties. By doing this you are also helping protect your basement from the possibility of flooding during a storm, when storm sewers and combined sewers become overburdened draining municipal roads and downspouts connected to them, the chances for sewer backup of clean storm drainage or dirty sanitary sewage becomes a very real possibility. There is no guarantee that by doing this your sewer will not back up, but if everyone took the time to disconnect their downspouts, the chances of basement flooding would become less likely.
Proper Grading and Slope away from the House are Very Important
A cool, damp basement, musty smells, and maybe even mold or mildew on the walls are all indications of moisture getting into your basement. The main cause is likely poor drainage around your home that allows moisture to build up and remain in the soil around your foundation, and then work its way right through your foundation and into your home. Fixing drainage problems around your house can be a relatively inexpensive proposition, and it often come down to a couple of issues–how rainwater is handled and the grading or slope of your property.