They can. Say you have plugin one, with only this:
// Plugin one
$variable = "henk";
And then you have plugin two, with only this:
// Plugin two
echo $variable;
And now you activate these plugins, you will probably see the variable of plugin one echo’d by plugin two (at least it did here, but I don’t know what determines the sequence).
It’s probably best to use a sort of prefix like $my_plugin_variable if you’re not using it inside a function or class.