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We present the result of a series of contemporaneous (within one day) hard X-ray (Ginga) and ultraviolet (IUE) observations of the Seyfert 1 galaxy NGC 5548. Nine of these observations were carried out over a period of 51 days in 1990 May-July, and two in 1989. An additional simultaneous IUE-EXOSAT observation obtained on 1984 May 21 is also analyzed. In 1989-1990, the 1350 A continuum and 2-10 keV flux both varied by a factor 2.6 in a highly correlated (at better than the 99% confidence level) fashion. Adding the single 1984 data point significantly weakens the correlation, since the UV flux was 3.5 times larger then than its average 1990 value, while the X-ray flux was only 70% higher. In 1990 the UV and X-ray flux variations appear to be simultaneous to within a few (<= 6) days. These results, together with the simultaneity of the variations at 5000 and 1350 A, are incompatible with the standard geometrically thin accretion disk model. To salvage the disk model, one must postulate the existence of at least two continuum emission components in the UV-optical regime. The first one arises from thermal reprocessing of the X-ray impinging on and absorbed by the disk, while the other represents the thermal emission generated by viscous processes inside the disk itself. In this scheme, the reprocessed component varies in phase with the hard X-rays and accounts for the bulk of the UV emission when NGC 5548 is in a low to intermediate state of brightness, while larger amplitude variations are driven by a change in the amount of gravitational energy released locally inside the disk. The thermal reprocessing region extends to at least 200 Schwarzschild radii, much further out than the UV-emitting region in a standard disk without reprocessing. Since the relationship between the UV and the X-ray source in NGC 5548 is phenomenologically identical to that in NGC 4151, this scheme may be applicable to Seyfert galaxies as a class.