Yes, I've noticed a lot of grain in some of my scans also, especially from negatives that produce higher grain to begin with.  For example, the higher the ISO number, generally the more apparent grain you will see. Good film at 100 ISO or below produces little apparent grain at moderate sized enlargement while ISO 800 will show more.  I believe that grain is also more apparent in negatives than positive (chrome/slide) films.  The other thing I have heard is that scanning resolutions at 5000ppi and above somehow avoid magnifying the grain that you and I see from our scans.  Unfortunately, my film scanner maxes out at 4000ppi.

Another solution is to use a scanning software that has built in grain reduction. A German company (Lasersoft) produces a scanning software called Silverfast Ai that has a built in grain reduction program that works very well.  I use it on my flatbed scanner for print scanning and medium format transparency scans.  Unfortunately, Silverfast is not inexpensive unless you get it bundled with the purchase of a scanner as I did.  I've been toying with the idea of obtaining it for my film scanner, but it runs over $300, and it's good for just the one scanner.  Each scanner has its own version.

You might try scanning at a lower resolution and see what effect that has on reducing grain. In Photoshop try using the Filter>Noise>dust&scratches or the median filter.  Also be sure to buy low grain films to begin with.  Check manufacturer's or photo web site for stats on products.

I used these two filters on the photo below.  First pic is the untouched version.  The second is dust and scratches, and third is median. Both filters seem to blur details somewhat depending on how you set them, so be careful and be prepared to use a sharpening method to bring back detail.  By the way, this photo wasn't all that sharp to begin with and before cropping, this it included the whole animal and quite a bit of background.. Sharpening is also necessary for scanned photos/transparencies that will be used for books/magazines, etc, in order to get the best product, but that's a whole complicated subject by itself.

I can swear there ain't no heaven but I pray there ain't no hell. _ Blood Sweat & Tears