Genesis 9:11

 "I establish my covenant with you:  Never again will all life be cut off by the waters of a flood; never again will there be a flood to destroy the earth."  Genesis 9:11

God is promising this to all the creatures of the earth and all the future creatures to come.  There will never be another flood that will destroy all life on the land.  God did not just make this promise to Noah and his family, but to all the animals too!  Even though they were not made in his image like man was, he still loves and cares for each animal.  No matter how bad mankind might get again, he's promising the animals that he won't wipe the earth clean with another global flood.

Genesis 9:8-10

 Then God said to Noah and to his sons with him:  "I now establish my covenant with you and with your descendants after you and with every living creature that was with you - the birds, the livestock and all the wild animals, all those that came out of the ark with you - every living creature on earth."  Genesis 9:8-10

The first seven verses of the chapter started as God giving a blessing to Noah and his sons.  Now in verse 8, God is speaking to them and establishing his covenant with them and all the living creatures on the earth.  So the first seven verses were just for mankind and now this covenant is for all creatures on the earth, not just the men.

Genesis 9:7

"As for you, be fruitful and increase in number; multiply on the earth and increase upon it."  Genesis 9:7

Here, God is echoing the same instructions he gave Adam and Eve in Genesis 1:28 when he first created mankind and blessed them with life.  He wants humans to thrive and expand.  Despite his earlier punishment, God still loves mankind and wants good for us.

BibleRef points out that this is following God's harsh stance against killing.  Not only are humans made in his image (as reiterated in verse 6), but he wants to stop the kinds of violence that ruined the world before the flood.

He's not still holding a grudge, saying "Okay, you survived my punishment, but lets see if you make the final cut."  No, God is telling them that they have a fresh start, the world's slate has been wiped clean, now go forth and live.  In the same way, we make mistakes and sin.  Then we repent and ask for forgiveness and God (through Jesus's sacrifice on the cross), gives us that forgiveness.  Our slate is wiped clean, now go forth and live.