So I just did a bit of research for my geography class:

Thomas Malthus was an English scholar born in 1766 (died in 1834). In 1798 he published a book that criticised the views of people who believed life would improve for humans on earth. His main argument was that because of the natural human urge to reproduce human population increases geometrically (1, 2, 4, 16, 32, 64, 128, 256, etc.). However, food supply, at most, can only increase arithmetically (1, 2, 3, 4, 5, 6, 7, 8, etc.). Therefore since food is essential to human life, unchecked population growth would eventually lead to starvation.

Ester Boserup was a Danish economist born in 1910 (died in 1999). In 1965 she published a book that criticised the assumption made by Malthus that agricultural methods determine population via food supply and instead argued that population determines agricultural methods. Her main point was "necessity is the mother of invention"; meaning we would always develop new technologies as long as they are needed. 

I'm kindoff in the middle, I think if the global population grows steadily, then we'll have enough time to develop technologies that can help provide enough food for everyone. But if the population grows rapidly, then we may not have enough time to develop the tech we need and wars over food/water could become common and many more people will die of starvation. 

What do you guys think? Is there a limit to how much we can produce? Will technology used in agriculture progress fast enough?

You are missing the point that Malthus died before the Green Revolution occured which allowed for mass production of agriculture. There is a limit to population growth as we will eventually use all farm land to live. Therefore the alternative would be to live in the sky and grow on earth so population growth can grow forever (Bioshock infinite?)..

I can't remember who said it, but it was something to the effect that we could fit nearly 100% of the world's population in the state of Texas with roughly the same population density as New York City if we really wanted to. Population growth is not the problem ... quite the opposite when one considers a vast majority of people in some countries are aging and will be dying off in droves with not nearly as many people in the generations that follow them to make up the loss. It has been awhile since I have looked at statistics for this sort of thing, but that is the general impression I have.

Forget about colonizing the sky (I can only imagine how challenging that would be) we need to go the Bioshock 1/From Russia with Love way with seasteading either through underwater cities or above water cities (seasteading). This seems far more practical than cities in the sky or colonies on the moon or something as you have a food source (fish seaweed plants ect.) and a source of energy (solar, wind, geothermic ect.) and easy transportation we already have mastery over (boats, submarines, underwater trains ect.)

Yeah, colonizing the sea will be next, or building artificial islands. In the distant future (100+ years) Space will be the next option, either moving people on to huge ships, terraformimg mars (far-fetched but possible) or colonizing an earth like planet, but we'll need to make some incredible progress in space travel technology before that's possible. WIth current technology, I heard it would take 19,000 years to get to the nearest star outside our solar system xD 

The problem with these prediction is that new technologies would come along and solve problems that never would have thought of possible.

If all else fail, drop a few bombs here and there and you've got the population controlled.

In the long long term space will be our only option when the sun goes supernova in 5 billion years (less than that considering it will become so large that Earth will no longer support life ... which is a fun fact to throw at environmentalists since no amount of conservation will save this planet). Hopefully, we will be long gone by then in another solar system or maybe spread out over several.

Another way of looking at the space travel thing is that we are thinking about it from a short life span (70 -80 years) life span. Even with no progress in space travel technology we might still have a chance so long as we can invent technologies to stop aging or at least some sort of stasis pods like you see in a lot of sci-fi that let us stay asleep for the very long journey to a new solar system.

From what I know about terraforming we should really start going for that soon since the process can take centuries to complete. Should try it on Mars ... is not like we are going to make the planet less livable or anything.