Brewing day
-----------
* **Sanitizer** - To sanitize all of your equipment.
* **6 gallon fermenter** - For primary fermentation.
* **Funnel or Tubing** - To transfer from the brew kettle to the fermenter (pour or siphon)
* **+3 gallon brew kettle** - For boiling the mixture and making wort
* **Thermometer** - To monitor the temperature of the wort
* **Hydrometer** - To test the original gravity of your batch
* **Paddle/spoon** - Something to stir the boil with
* **Timer** - You need to know how long to boil and when to add ingredients
* **Ice** - After brewing, you will need to cool the wort. Putting the kettle in ice water to cool it faster

Transferring day (if you transfer)
----------------
* **Sanitizer** - To sanitize all of your equipment
* **5 gallon fermenter** - For secondary fermentation
* **Siphon tubing** - To siphon the beer from your primary fermenter to your secondary
* **Fermenter airlock** - To lock oxygen out of fermenter while allowing other gases exit

Bottling day
------------
* **Sanitizer** - To sanitize all equipment and bottles
* **Bottles/caps** - Make sure they are not twist-off bottles
* **Bottle capper** - How else did you expect the caps to get on?
* **Bottle brush** - If the bottles aren't clean, you'll need to clean them
* **Siphon tubing** - To siphon beer from fermenter to bottles
* **Thermometer** - To check temperature when recording final gravity
* **Hydrometer** - To measure the final gravity
* **Priming sugar** - Used to carbonate the beer while in the bottle
* **Bottling wand** - This allows you to easily control the flow while bottling

Nice to haves
-------------
 * **Auto siphon** - This will make siphoning a breeze
 * **Log sheet(s)** - Keep track of what you're doing. This is science after all!
     * http://cdn2.brewersfriend.com/brewersfriend_extractsheet.pdf   
     * https://web.archive.org/web/20160804111221/http://homebrewmanual.com/media/Home-Brewing-Record-Sheets.pdf   
 * **Checklist** - Don't forget anything!
     * http://cdn2.brewersfriend.com/brewersfriend_checklist_extract.pdf

This list is mostly if you plan on doing extract brewing. You might need extra equipment for a full-grain setup. Also, this assumes you are using a kit that comes with necessary ingredients and a muslin bag.

Brew kits, which should supply much of the equipment, are available from various homebrew shops.