Depends on what tomato you are growing, but most of what I've read says nothing smaller than a 5 gal.

I use pots all the time -easier for me to care for
also my raised bed- this yr lettuce carrots and strawberries are taking over the bottom section will soon take over my cucumbers

Thanks so much, nmr82. My garden is so crowded, I am getting desperate for solutions.

I'm using 5 gallon buckets for all my tomatoes this year. I grew some in Grow Boxes last year, which are a little smaller than 5 gallons, and they grew fine.

This year I am growing about 4 tomatoes in pots and they are determinants. All are in about 5 gallon soil. So I cannot say for sure how they should perform. But then there are people who would say anything less than 10 gallon is too small. Then we here a lot of gardeners who grow them in 5 gallon buckets all the time.
Definitely, bigger container has advantages but the question is : IS IT ABSOLUTELY A REQUIREMENT ?
When growing in smaller containers, your job is more difficult ; have to water it more often, have to fertilize it more often, watch out for hot weather, as the soil in smaller pot would heat up faster. Also providing support in a small container is more challenging. So to me it is more about grower/gardener's convenience than what the plant needs. Plant needs water and nutrients. It is going to be happy if it gets what it needs.
So having said all that , I would not grow a huge indeterminant in a pot. Somehow, there has to be a proportion between the plant's foliage and the container. The way to achieve this is choosing a smaller variety and/or pruning systematically.

I always grow one Sun Gold in a 15-gallon container on my back deck. It turns into a 10 - 12 foot monster, sending vines onto the roof and scrambling up into the Liquidambar tree nearby. Here's my set-up.

Josh

I've tried tomatoes in containers many times, and I always have better results if they have more root room than, say, a 5 gallon container can provide... but that's not to say it can't be done.

I think the key factors will be nutrition, light, and water. If you can provide those in plentiful amounts, and you go for a more porous medium, I think you can have great results.

Check out Tapla's article on the front page... for pertinent info.

Here is a link that might be useful: Container Soils - Water Movement and Retention XIX

This is my first year using drip irrigation. It makes a world of difference. Without any stress days, they thrive.

I grow tomatoes in flower pots on my patio every year. Most of my pots are 5 gallon, some a little smaller. Like others said, the smaller the pot, the more vigilant you have to be about watering and feeding. In my experience, even a giant tomato plant doesn't have a massive root ball. I don't think it needs a lot of root space, it's just about it being more work to meet the needs of the plant with less soil being much quicker to dry out. My best pots are containers from Loll Designs. They are expensive, but they are thick plastic made from recycled milk cartons and seem to be the best job of retaining moisture and keeping the soil from cooking in the heat.