Vim Auto Indent with newline

I found that delimitMate does exactly what you describe and more (that is, automatically inserting the ending }). Note you have to tell delimitMate to expand carriage returns by adding let delimitMate_expand_cr=1 to your config.

From my observation, this is exactly the behaviour found in TextMate and SublimeText.

I have Ubuntu 12.04 and I found no vimrc file in home directory. Global vimrc file was in /etc/vim/vimrc.
There was almost nothing in this file. So for me it worked to add this 3 lines to the end of /etc/vim/vimrc

set autoindent
set cindent
inoremap { {<CR>}<up><end><CR>

When you will type { next time it will be changed by combination {, Enter, }, up, end, Enter. cindent and autoindent will add required amount of Tab's.
P.S. I'm not good in tuning up vim so some explanations may be not so accurate. It's how I think it works.

Put this in your .vimrc :

imap <C-Return> <CR><CR><C-o>k<Tab>

Assuming autoindent and smartindent are set correctly, typing Ctrl + Return between braces will put your cursor where you want it to be.

autoindent refers to it carrying over the current indentation level onto subsequent lines. To get it to indent according to syntax, you need to specify a flag like smartindent or cindent as well.