As with any classic car, this is difficult to answer given the variety of conditions of vehicles out there. But if I was pushed to commit to any statement it would be this:
Yes, because they're so damn simple not much can really go wrong.
The engine is particularly bullet proof and had a very long production run (up until 2009 in South Africa). The injection system (if your car has one) is a mechanical Bosch unit that was so popular it was used by a wide variety manufacturers from Rolls-Royce, to Porsche, to Ford. The electronics are dead simple, mostly because there really isn't any.
The main things you've got to watch out for is general wear and tear on the engine and running gear, and rust but if the example you're thinking of purchasing has been well looked after than these should be less of a concern.
Let me make one thing clear, though...
These are still old cars. They will never be as reliable as a newer car. Technology, precision, and manufacturing techniques have come a long way in the 50 years since the first Golf was made and it's just not reasonable to expect a 50 year old car to be as reliable as a 1 year old car.
Personally, with my car (a 1993 Cabriolet), I've found the following to be problem areas:
Rust is the largest cause of concern when owning an older car. Obviously, this varies depending on how well the vehicle was kept and where it spent its life. It's worth noting too that later model Mk1s received better rust protection and alterations to trouble-prone areas.
Common rust areas
Less common rust areas
Absolutely. If you don't mind lack of air-conditioning and power steering (not an option on most models). As long as you're willing to address issues as they arise and accept that they will be more frequent than a modern car, then there's no issue with dailying a Mk1.
Whilst you're not going to win any drag-kudos when the lights go green, acceleration is adequate if the car has the "big-block" 1.8lt engine and cruising at highway speeds is fine, particularly if you've got the 5 speed manual. With a surprising amount of torque for a car this type at higher speeds, overtaking is not an issue either. Remember, though, that by today's standards it is not a fast car. But it will surprise you how capable it is.
Having non-power assisted steering is an annoyance in parking lots, but otherwise the rack and pinion steering is quite tight and nippy, though the addition of a strut brace noticeably improves things.
The car pretty much drives how it looks - simple and light, cheerful and engaging.
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