Beth's Discs
Cyclone 162 g? Discraft As stated below, everyone needs a Cyclone.  Beth uses this disc for everything except short-range putting.
Upshot 173 g Lightning My first putter.  It was a good putter but Beth needed a putter, so I gave it to her.
Leopard 162 g Innova No, we've never been to Oak Grove Park.  I got this with a few others in a golf disc grab-bag of sorts.  I gave it to Beth, and she doesn't use it too much.

Josh's Discs
Valkrye
Champion
Edition
167 g Innova My primary driver.  Hard plastic makes this disc very durable.  Predictable flight and good distance.
Cyclone 165 g? Discraft My primary approach disc.  Everyone should have a Cyclone.  It makes a great first disc for a beginner, and it's a great mid-range driver or approach disc for more experienced players.  Extremely predictable.
X-Clone 176 g Discraft I use this disc exclusively for hammering, which I do quite often.  I bought this disc when my old 150-class X-Clone hammered a few too many trees and started wobbling.  This disc produced my first (and only) hole-in-one.
Birdie 175 g Innova My primary putter.  A good short-range putter that will fly straight.  It won't usually float on you, but that also means it has a tendency to fall short on longer putts.
Cheetah 150 g Innova This is my third 150-class Cheetah, having lost the previous two.  The lightweight cheetahs will fly forever when there is little or no wind.  However, they can be easy to lose when there is quite a bit of a breeze (trust me on this).
Whippet 174 g Innova The first driver I ever had, and not one for beginners.  I'm lucky this didn't discourage me from continuing to disc golf.  Very overstable.  This thing will cut through the heaviest wind, but isn't particularly easy to control.
Gazelle 170 g Innova My second gazelle.  I never particularly liked my first one.  We found this one  (probably at Gateway, but I don't remember), and I'm not sure I've ever thrown it.
Python 175 g Innova This disc is supposed to fly in an S-curve.  I don't know about that, but it's a great disc for hammering:  it kind of floats rather than taking a dive into the ground like the X-Clone.  However, it's not as good at flying over or through things.
Hammer 175 g Innova My first approach disc, along with the XD.  The two discs are very similar, and neither is a good beginners disc.  However, they are both very maneuverable and great for experts.  I am not exactly an expert yet, though.
XD (aka
Aviar XD)
175 g Innova See above.
Aviar 162 g Innova A good beginner approach disc.  I never really got into it.
Aviar Putt &
Approach
147 g Innova See above.
Polecat 169 g Innova A good distance putter.  If I carried two putters, this would be the second.  I've had more luck with the Birdie, so I use that one primarily.
X-Clone 150 g Discraft My original hammering disc.  It got beat up a bit too much (never use a 150-class disc as your everyday hammer disc) so I retired it.
Eclipse 181 g Discraft An interesting disc that I've used a few times but haven't gotten around to really knowing.  I need to take it golfing sometime.
Elite Pro XL 167 g Discraft This was my primary driver for a while.  It flies long and straight.  We found it at Gateway.
Elite X-press
1st Run
169 g Discraft See Eclipse.
Stratus 175 g? Discraft We found this at Dorey Park in Richmond, VA.  I've never used it.
#1 Slice 165 g Lightning See Eclipse.
#1 Roller 170 g Lightning See Eclipse.
JLS 1.2 174 g Millennium We found this at Gateway Park in Ames, IA.  I've never used it.