Know that your child is not being unreasonable -- you are! Babies at this age have no idea that anyone else might have wishes and feelings similar to their own. So you can't expect him to wait for a toy that is sitting right in front of him -- and looks so fun to play with!
Play follow-the-leader. When your little miser takes a toy from another baby, you can gently say something like, "No grabbing. That makes Sabina sad." See if he returns it on his own, but don't snatch it back -- babies learn from our actions, and your grab will only teach him to do the same. Instead, offer the other child a new toy; watching you soothe a sad baby will give your own little one ideas, and he may try to emulate you in a few months.
Lay down the law. When your baby wants to keep all the goodies for himself, tell him to choose one or two and share the others. Most of what you say will go in one ear and out the other, but do try to be polite before handing over the rest of the toys for public enjoyment. He may cry, but he can't play with them all at the same time anyway.