That's a difficult question to answer. Some re-makes are actually good, and are very enjoyable to watch. Some are faithful re-makes, others put a new spin on the original, like this summer's re-imagining of Halloween. Both faithful re-makes, and re-imaginings can be very good.
On the other hand, some re-makes can be an absolute mess, and really should not be made. They add nothing new, and can actually almost taint the name of the original.
On balance, I'd say they should still produce re-makes. They do result in some poor films, but I think that's acceptable if we get some good modern takes on older films in return.