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.