Base layers have nowadays become as much a part of sports kit, particularly football as the shirts themselves. Contrary to popular belief these are not worn by the top players like Wayne Rooney just for show, there is scientific evidence that suggests that wearing base layers improve performance.
Wearing a tight-fitting base layer especially when playing football helps to keep your body at the right temperature when playing sports, they aide to wick sweat away from your body. Due to the second skin nature of a base layer they also keep your muscles in line, preventing injury.
Of course these days the big sports wear brands like Nike and Under Armour have produced a host of all singing, all dancing options with added pads and protection. These are of course great for targeted sports but keeping it simple and investing in a few core options will see you through from sport to sport.