Help with a simple comparator circuit
Olin and Russell already explained that your thermistor value is too low: it will dissipate 820mW and make any temperature measurement impossible. I found a nice 50k\$\Omega\$ NTC thermistor, which may be better suited; it dissipates 1.6mW at 25°C. If you don't like it, don't worry, I'll go through the necessary calculations, and you can follow them with your own NTC. 

 

I'm assuming you want to set the thermostat between 20°C and 30°C, with thermistor values of 63k\$\Omega\$ and 40k\$\Omega\$ resp. (I found those on p.12 of the datasheet). If we choose 50k\$\Omega\$ for R8 we have an input range for the opamp of 4V at 30°C to 5V at 20°C. We're nicely in the middle of the power supply range, and we won't need a Rail-to-Rail Opamp.

Let's follow Russell and pick the LM324 for the opamp. Not just to please Russell, it's also one of the cheapest, and we'll use the other three opamps in it as well.
The LM324 from Fairchild's input common range goes to \$V_{CC} - 1.5V\$ at 5V supply, so that's OK. Also the lower limit is OK; the LM324 accepts voltages down to 0V.  

Let's look at that other voltage divider with the potmeter. If we want to control between 4V and 5V we can easily see that 40k\$\Omega\$ + 10k\$\Omega\$ potmeter + 40k\$\Omega\$ gives us the right range. Let's use 39k\$\Omega\$ for that.  

Then there's the feedback resistor for the hysteresis. We have an input voltage variation of about 1V/10°C, so if we want a 0.5°C hysteresis, we have to move our setpoint 25mV up or down. I'll cut some corners and assume \$V_{OUT}\$ of the opamp goes from 0V to 9V. We set our potmeter in the middle. Then for the high threshold we can use KCL:  

\$ \dfrac{9V - (4.5V + 25mV)}{44k\Omega} + \dfrac{9V - (4.5V + 25mV)}{R_{FB}} = \dfrac{4.5V + 25mV}{44k\Omega} \$

and solve for \$R_{FB}\$ we find a value of 3.94M\$\Omega\$.
So now we have a thermostat we can control between 20°C and 30°C with a 0.5°C hysteresis.

Now the relay. Olin says the opamp can't drive that. He's right for most relays, but I found this one which only needs 11mA in the high-sensitivity 9V version. The LM324 datasheet says it can sink at least 10mA, so that's still not enough. But we have 3 unused opamps in the package, let's use them in parallel. The \$4.7\Omega\$ resistors make that the current is nicely distributed over the three opamp.  

It's possible that this has only academic value. We saved a transistor, but we needed two extra resistors (still cheaper). But the relay may be much more expensive than one with a higher current rating, and then Olin's solution with the transistor is better.