I couldn't possibly not have a page of free stuff - there is alot out there (big thank you to everyone that provides freebies!). It's possible to create digital art without it costing the earth. And free (or open source) doesn't mean 'no good'!   Here are some great links which I hope you'll find useful:

DAZ STUDIO  Provided by It's a fantastic 3d program that comes with some basic models and figures. You can create scenes,render, animate and more it,  and export  to Bryce, Hexagon, and Carrara.
GIMP  A free open source imaging editor. It's very much like Photoshop, but free!
BLENDER Another free, open source program for 3d modelling, animation, rigging and rendering.
BRYCE 7 This is currently free so grab it whilst you can!

IMAGE AFTER Has a very large collection of free images.
MAYANG  A great site focusing specifically on texture images.
MORGUEFILE No, nothing to do with dead bodies -just stacks and stacks of free images
BLENDER have provided a great set of public domain textures. 

RENDEROSITY has a large collection in different formats including for Bryce (you have to become a member to access the free stuff, but membership is free!)
DAZ3d has some great figures for starting out with Daz Studio or Poser. If you are a member you can also take advantage of the freebie of the week if you set your membership preference to get notifications.
ARTIST3D.COM has high quality models made for 3d Studio Max so they are in 3ds format - but Bryce can open that format so they shouldn't be a problem.
FREE3D has a nice collection of everyday objects for Bryce
TOUCAN You can find some lovely flower models here. They are compatable with Poser so you can load them into DAZ Studio and then import them ready textured into Bryce.
FAST3D   A fantastic collecition of everyday objects in Poser format (see my comment for Toucan)  to use in your scenes. You can also find some of them at Renderosity (under the name geralday)
Don't forget - if you use DAZ Studio in conjunction with Bryce you can use Poser models which will import into Bryce ready textured. Other object imports into Bryce i.e not using DAZ Studio, can be in .3ds .lwo,  .cob, or .obj format which won't be textured, you'll have to apply the texture in the materials lab. But it does mean you there is a great wealth of free models made in other programs that can be used in Bryce, such as 3ds Max or Cinema 4d.

NB Be aware of any licensing restrictions the models may have if you are going to use them in commercial renders.