What do you guys do with them?  Put them on characters who are already strong in that department so they get their faster/higher or put them on characters weak in that area?

For example giving Boyd a  Knight Band to improve his Defense.

If I plan to move these characters on to Radiant Dawn does that matter?  I really didn't understand the transfer system.  Sounded like you get growth bonuses for characters whose exp you've maxed?

Here's the explanation of the RD transfer stuff:

http://serenesforest.net/fe10/transfer.html

The gist is that, if you hit final level with a character, all capped stats will have bonuses in RD.

Makes me think i'll want to give the bands to characters who are likely to cap their stats anyway just to make sure i don't get screwed then eh?

Well the bands aren't really that great.

http://serenesforest.net/fe9/accessories.htm

+5% growth for 38 levels = +1.9 average stat points
+10% growth for 38 levels = +3.8 average stat points

I suggest you use them on units who almost cap things. If an extra 2 points means the difference between a bonus and no bonus in Radiant Dawn, why not?

Yeah, I noticed that. 

Makes me wonder too if I should check out the "Fixed' numbers and see who caps based on that.

I dunno I always go with random over Fixed... it has a chance to screw you but it makes the game more interesting to me.  You never know who's going to payoff.

Edit: Holy crap the Knight Ward is better then i thought it was.

Obviously using the band that increases strength on boyd won't help... but defense or soren would. Use it on good characters who have important stats that they won't cap.

I always just left them where they were, but that was because i usually used the characters that they initially came with. The original Greil Mercenaries were all good, except Mist and Rolf.