It really depends on what you intend to do with the resulting scans;
and, if you're making prints, what the maximum-size of print you're
capable of making (or may want to make in the future).  If you're not
going any larger than, say, 8x10", the resolution of your present
scanner should do (provided you're satisfied with the scanner's
performance otherwise).

The "best" DPI to use is, IMO, the maximum you've got - scan it once
that way, do whatever corrective work you feel the need to perform, then
saveit (preferably in TIFF format) via the storage medium of your
choice.  When you're ready to print, you'll have a file that should
print well from 8x10" downwards.  If you want to make a small file for
e-mailing or uploading to a website, you can make a smaller JPEG copy
from the original file.

Of course, if you have a hankering to print bigger than 8x10", a
higher-res scanner is more justified, and at the moment there are a fair
number to choose from - the "median" point now is around 3200-3600dpi,
and can be had for as little as $300.  More money gets you higher
resolution (the Minolta 5400, which I currently use, is the leader of
the pack at the moment at 5400dpi) and time-saving features such as
Digital ICE (for dust and scratch removal), and batch-scanning.  Again,
it all boils down to what you want to do.

Hope this helps.

4000 dpi would cover it very well.  A nikon 4000/5000, Minolta
DSE 5400, Scan Dual IV (3200 dp), etc.

Consider whether ICE would be a benefit to you as well before you
buy.

OTOH, as the other poster says, what is the end use of the scans,
if it is for printing, then the print resoultion drives the scan
resolution.

eg: a 300 dpi print for a 8.5 x 11 requires 3300 dots from 36mm
of frame ... about 2300 dpi.  If that is sufficient, then you're
there.

Cheers,
Alan

The major issue here is not resolution, but grain aliasing.  You can
do a google search on the subject and find a lot of hits.  If I
remember correctly, when the scanning resolution is about the same as
the grain size, the grain is emphasized.  I had that problem while
scanning at 2400 dpi.  For that reason my digital  pictures at 6
megapixels from my drebel are much better than scanned nagatives, even
though the result is a 8 megapixel image.