Before you buy something, try Audacity.
 
http://wiki.audacityteam.org/wiki/Noise_Reduction
 
I use Audacity, never used this effect, but for free, it doesn't hurt. Maybe it'll work, maybe not.
 
If it does not do what you want, then look at more expensive stuff.
 
My 0.02
 
EDIT: Ooops, Karyn was faster than me, sorry!

I've used it before on tape hiss,  it's very effective.
 
You select a small area with just noise and sample it, then the noise reduction effectively removes that sound from the rest of the clip.  You can vary the strength so it's not an all or nothing deal and it works very well.
 
If you have background noise like air conditioning hum or computer fan noise it will remove that as well.

If this noise is permanent, you can try the following idea:
-Look for a peace on your tracks where only the noise appears.
-Record that on another track.
-Turn the phase of this track
-play both tracks  and adjust the volume of the "noise track "
till the noise disappears - this must be at the volume  of the noise
from original track.
-if this works, copy the noise track till it´s as long as the original .
-bounce both tracks

Sorry , just saw that gswitz had the same idea.

I haven't tried Audacity but I tried all the Waves stuff and a few freebies that I can't remember the name of. Five minutes with RX3 and basic presets convinced me of its value. Just saying. As always, your mileage may vary.

+1 to iZotope RX.

I prefer this VST over the waves noise reduction stuff: http://wavearts.com/products/plugins/mr-noise/
Although I have used BOTH in-line together for the best result.
 
For stand alone, its hard to beat the iZotope RX

Start with the source. If you're handy with tiny screwdrivers and have some understanding of setting azimuth on the reel-to-reel tape head, you can adjust the alignment/azimuth of the reel-to-reel to get as clear of a signal as possible.
 
Then Google some free or cheaper versions of these: http://www.waves.com/bundles/restoration
Here's a suite that's only $99. https://acondigital.com/p.ducts/restoration-suite/
Here's that Soundsoap offering for $149: https://sites.fastspring.com/soundnessllc/instant/soundsoap_4

djtrailmixxx
...For stand alone, its hard to beat the iZotope RX...

I agree. I video taped a relative's outside wedding. The audio was covered with several noise sources, including a twin engine plane flying overhead. iZotope RX5 made it all better.
 
Walt 
 

Wow... what a great community!  One day and I have some great ideas to work with!
Thanks - all of you!  I hope to get started within the next few weeks.
Guy