Leave it standing -
If it's not disturbing you in any way, and it's stable, then there is nothing wrong with leaving the tree standing.
Free firewood -
If the tree is dead anyway, you might as well use the wood to keep you warm in the winter.
Sell it -
Contact a local company and sell the lumber. Depending on the type of tree, you might even make some good money!
Hanging bird feeder -
Use your dead tree to feed the local birds. Hang a bird feeder and see them returning every day to your garden.
Seat -
Tree stumps make great seats. If the tree is thick enough, you can also turn it into a coffee table. You can sand and varnish them for a nice finish.
Planter -
Cut a hole in the stump, fill it up with soil, and voila!
Bench -
A wooden bench can be as elaborate or as simple as you want it to be.
Borders -
You can cut your dead tree and use the wood to build garden beds or walkways.
Stepping "stones" -
Simply slice up the tree trunk and use the wood as garden stepping stones.
Stamps -
Use the old wood to create a stamp set for your kids to play with.
Bird-nesting box -
Give the birds around your house a nice cozy space. It's always nice to have wildlife in your garden.
Birdbath -
You can hang a birdbath on the tree or even carve one if you want to.
Floor lamp -
You can use branches to build a lamp. Let your creativity (and electricity) flow!
Wall clock -
You can easy build one, even if only for decor purposes.