There are two common, modern, systems that do not use a rocket.
The Carl Gustav 84mm (in use in the US as the M3 MAAWS) and the related AT4 (variants in service across the world, most notably in service with the US as the M136.
Both are recoilless rifles.
In addition, the obsolescent German Armbrust system is a counter-mass gun.
Interestingly, RPG7 has a boost/sustain arrangement where an initial motor pushes it out of the tube and a second motor burns throughout flight to keep the speed up. This has some advantages including reduced launch signature compared to other systems that burn their propellant entirely within the space of the launch tube, but also has flaws. Most particularly, the trajectory in any kind of cross-wind is reportedly somewhat difficult to judge.