Not every mechanical problem with your car means that it should be towed; sometimes you can still control your car even when it's running a bit rough. However, since it's never good to take a risk with your safety and the safety of other drivers when on the road, you might note when it's best to stop driving and have your car towed, either home or to a repair shop.
If your car skids when you brake, this is not something to ignore. A brake pad could be slipping and gripping a wheel unevenly so that wheel pulls and causes the car to skid. If the brake pad slips entirely, it could wedge itself between the tire and rotor and your car could slam to a stop when you least expect it.
If your car skids when turning, this could be a worn differential. These are gears that allow the car's wheels to stay the same speed even when traveling different distances. When you turn a corner, the inside wheels are traveling less distance than the outside wheels. The differentials keep them in sync and when the gears wear, one tire is then spinning faster or slower than the rest and the car will skid or pull. This too can be dangerous as it's difficult to control your car around turns when the differential is worn, and the car should probably be towed in this case.
If your car takes a few seconds to move when you put it in gear and then it seems to lurch forward, this is usually low transmission fluid and refilling this fluid may take care of the problem. However, if your car shudders and lurches regularly when you drive, this often means the fuel and oxygen ratio are not right. The car may not be getting enough oxygen to create combustion; in turn, it's burning added fuel and causing the engine to run irregularly. The car could easily stall and not start again in this case; have it towed and have a mechanic check the oxygen sensor or throttle box for repair.
If the shuddering you're having with your car means extreme shaking of the steering wheel, and especially if you can feel one particular wheel shaking violently, this can mean a bent rim. This can keep you from controlling the car when you steer and especially when you turn. It's good to have the car towed and have the wheel in that corner checked for a needed new rim or alignment and balancing.