Film doesn't really have inherant "Resolution". When evaluating its sharpness we refer to its "resolving" power. This is dependent on many factors, mostly format (ie 16mm, 35mm, 65mm), lens quality and film stock. The bigger the format, the higher the image quality can be because its captured on a bigger area (ie 35mm is twice the size of 16mm, therefore its detail should yield double). Lenses probably make an equal difference, but most people don't consider this; some lenses are softer, some sharper, and it contributes greatly to the amount of detail captured. As ChainsawAsh stated, film speed plays a role as well, as fine grain, typically low speed, film can capture greater detail. Even things like shooting aperature can contribute to resolving power, since contrast levels change with your aperature.

All in all, its estimated that, under the best conditions, 35mm ideally resolves something like 5 times the amount of your standard 1080-HD. HD is really equivalent to modern 16mm. There's this perception that 16mm equates grainy old soft documentaries but nothing could be further from the truth.