Whether or not you choose to buy is a complicated question. I will answer as "what you should consider/think about" as I don't think "What should I do" is on topic.
First off, renting tends to look expensive compared to mortgages until you factor in the other costs that are included in your rent.
Property taxes. These are a few grand a year even in the worst areas, and tend to be more. Find out what the taxes are ahead of time. Even though you can often deduct them (and your interest), you're giving up your standard deduction to do so - and with the low interest regime currently, unless your taxes are high you may not end up being better off deducting them.
Home insurance. This depends on home and area, but is at least hundreds of dollars per year, and could easily run a thousand. So another hundred a month on your bill (and it's more than renter's insurance by quite a lot).
Upkeep costs for the property. You've got a lot of up-front costs (buy a lawnmower, etc. types of things) plus a lot of ongoing costs (general repair, plumbing breaks, electrical breaks, whatnot).
Sales commission, as Scott notes in comments. When you sell, you're paying about 6% commission; so you won't be above water, if housing prices stay flat, until you've paid off 6% of your loan value (plus closing costs, another couple of percent). You hit the 90% point on a 15 year about year 2, but on a 30 year you don't hit it until about year 5, so you might not be above water when you want to sell.
Risk of decrease in value. Whenever you buy property, you take on the risk of losing value as well as the potential of gaining value. Don't assume that because prices are going up they will continue to; remember that a lot of investors are well aware of possible profits from rising prices and will be buying (and driving prices up) themselves. 2008 was a shock to a lot of people, even in areas where it seemed like prices should've still gone up; you never know what's going to happen. If you buy a house for 20% or so down, you have a bit of a safety net (if it drops 10-20% in value, you're still above water, though you do of course lose money), while if you buy it for 0% down and it drops 20% in value, you won't be able to sell (at all) for years.
All that together means you should really take a hard look at the costs and benefits, make a realistic calculation including all actual costs, and then make a decision. I would not buy simply because it seems like a good idea to not pay rent. If you're unable to make any down payment, then you're also unable to deal with the risks in home ownership - not just decrease in value, but when your pipe bursts and ruins your basement, or when the roof needs a replacement because a tree falls on it. Yes, home insurance helps, but not always, and the deductible will still get you.
Just to have some numbers:
For my area, we pay about $8000 a year in property taxes on a $280k house ($200k mortgage), $1k a year in home insurance, so our escrow payment is about $750 a month. A 15 year for $200k is about $1400 a month, so $2200 or so total cost. We do live in a high property tax area, so someone in lower tax regimes would pay less - say 1800-1900 - but not that cheap. A 30 year would save you 500 or so a month, but you're still not all that much lower than rent.