You can get your own place if you follow the main quest.
For this one you can also buy upgrades.
There is an earlier opportunity to rent a motel room (forever).
gaming.stackexchange.com/users/4103/Mad Scientist
There are two 'homes'.
When you reach Novac, there is a Motel room you can rent, which is safe to store stuff and rest in, and if you complete the quest One for My Baby by accusing the actual perpetrator, you'll receive it permanently at no charge.
Further along the main quest, once you reach The Strip, you'll be given access to the Presidential Suite at the Lucky 38 Hotel and Casino.
This functions more like the house you gained in FO3, in that when you dismiss companions, you can have them wait for you in the Suite, and you can purchase various 'upgrades' to add more style and functionality to the apartment.
There are also several mods that add additional crafting resources or other customizations, if you're playing on the PC.
gaming.stackexchange.com/users/3129/LessPop_MoreFizz
You also get a room for free at the Wrangler once you have collected every debt and taken care of the previous debt collector (which is the last task of that quest).
gaming.stackexchange.com/users/5022/wildpeaks
You can use Victor's shack in Good Springs: that's the first house you can get.
You've got a bed to sleep in, a sink which is purified, a oven to store your aids, a couple of ammo boxes to store weapons and ammo, and also a desk to store your miscellaneous stuff.
It's also free of charge; there's no need to rent a motel room.
gaming.stackexchange.com/users/None/
Get in a house, kill whoever is in there, and just stash your stuff there.
For example: Kill Victor (you are gonna do it anyway in the storyline, unless you are the kind of guy that does anything you're told and be House's dog) and take his shack.
Also, there are several abandoned places which would do just fine.
gaming.stackexchange.com/users/None/
All you need to do is find Harper's Shack.
It's just north and east of hidden springs.
It has a campfire outside for crafting, a reloading bench, a workbench, lockers, storage boxes and a bed.
The only downside is it's near a deathclaw cave.
Easily avoidable and/or assaulted
gaming.stackexchange.com/users/11079/Jessica
The Jean Sky Diving shack, down the road from Goodsprings, is also a good storage house with only two Powder Gangers and some Bloatflies out back.
gaming.stackexchange.com/users/29256/Brandon
There is also an unoccupied shack right next to a burial ground near Good Springs.
The only downside is there are a small portion of Radscorpians.
gaming.stackexchange.com/users/38202/Eric
There is a general store in Nipton, inside there is a harmless powder ganger.
Kill him.
The store contains a bed and a safe you can put your stuff in.
gaming.stackexchange.com/users/78116/Jeremiah Hill
I was wondering if you can get your own house in Fallout: New Vegas like you did in Fallout 3?
Can you get your own house?
gaming.stackexchange.com
<fallout-new-vegas>
gaming.stackexchange.com/questions/10305
gaming.stackexchange.com/users/2874/Lukasz
You need to follow the main quest. You can get a room for free at Wrangler, or use Victor's Shack in Good Springs. There is also Harper's Shack, Jean Sky Diving shack and an unoccupied shack next to a burial ground. You can simply follow the main quest. There are however a number of shacks and houses that you can accupy, like a room at the Wrangler, Victor's shack etc. There is also the option of using mods to add housing options of course.
User suggests following the main quest. There are a number of houses that can be occupied on the map, say players Mods can also add houses for the player.