Vim 7 has built in spellchecking. There are two easy ways to turn on spellchecking. If you are using Gvim, you can use Tools > Spelling > Spellcheck On:
If you are using Vim in the terminal, or prefer to type, you can turn on spellchecking in Vim with the command :set spell and turn off spellchecking with :set nospell.
Mispelled words will then be underlined in red in Gvim:
Or highlighted in using Vim in the terminal:
Here are the commands you need to know:
Here is the Vim spellchecker offering suggestions for the word Nihon:
That is Vim spell checking in a nutshell. For more commands and documentation, just type :help spell into Vim or read the Vim spell docs online.