A guitar.
This one is obvious, but it needed to be said. Ideally, you would get one custom made. Practicing woud be a pleasure with a perfect guitar!
If you are not certain that you're in for the long haul, buy a cheap guitar. You will be able to progress just as well, but without the initial outlay.
Fender Squires are popular choices for beginners.
Make sure you buy a strap as well. A strap will help keep your guitar in a good position, even while sitting.
An amplifier.
A small amp will usually be adequate just for practising, but sometimes it is wiser to spend a little bit more and get a more versatile amp for the future.
I started off playing without an amp, but it is not a good idea. It is hard to feel motivated when you are just listening to some plinky strings. Get an amp, turn it up, have fun!
Cable.
You're gonna need some cables to hook that amp up! Cables are cheap and although you do get what you pay for, unless you're recording you won't need super high quality cables.
A tuner.
When you play along to AC/DC's Thunderstruck on your first day of learning guitar, it won't sound very good if your guitar is out of tune. Invest in a good tuner, with proper care it will last you for a very long time.
Other/Optional.
A case or gig bag. Useful if you will be transporting your guitar.
Picks.
A headphone amp. Good for practicing late at night without waking your neighbours.
