My instinct tells me that it is used more often with the potential form of verbs than with the dictionary form.

(Quick potential review:

食べる        食べられる        can/is able to eat
行く            行ける            can/is able to go
する            できる            can/is able to do
)

Here is a comparison:

食べそう        appear to eat
行きそう        appear to go
しそう          appear to do

食べられそう    appear to be able to eat
行けそう        appear to be able to go
できそう        appear to be able to do

With the dictionary forms, it’s difficult (for me at least) to think up examples. I mean, either the person is or isn’t eating or doing whatever it is they are eating or doing. It’s a very objective judgment.

With the potential, on the other hand, you are making a subjective judgment about what someone (either yourself or someone else) appears able to do. I mean, sure, you’ve eaten twenty hot dogs before in an eating contest, and now, looking at the plate of twenty-five in front of you, it doesn’t look so bad, right? You could probably eat twenty-five. While you think you can eat twenty-five, you want to express a bit of that doubt and subjective judgment:

うん、食べられそうです。

In English, I might be comfortable translating this to the Thomas the Train Engine “I think I can.” In English “I think…” is often used to express the fact that you subjectively believe something to be true but are slightly unsure. It’s used this way in Japanese too, but perhaps not as often. And this tense is less hefty than attaching a big fat 〜と思います to the end of whatever it is you are out there thinking subjectively.

Here’s a funny story. On the night of the Shiokawa Fireworks Festival, I was driving from Shiokawa to Nishiaizu through Yamato and Takasato. For those who don’t know, the roads that go through Yamato and Takasato are mostly unlit mountain roads. As I came over one hill, a bigass tanuki appeared in the road. I was going reasonably fast for the road – 60 or 70 km/h – but I figured I was still far enough from the animal for him to move out of the way. He took his sweet time, however, and I realized I was going to hit the fucker! I slammed on the brakes and swerved, just barely missing him…I think. I didn’t hear any strange noises, so I don’t think I killed him. But it was really closed. I almost killed him.

The next day at school I was drinking tea with the office ladies and told them this story using the Japanese phrase 「ほとんど殺した。」, a direct translation of the English, which induced laughter in all Japanese present. I quickly realized the mistake but also realized that I didn’t know how to say what I wanted to say – I didn’t kill the tanuki but it was goddamn close. The phrase 「ほとんど殺した。」implies that I beat the tanuki to a bloody pulp but spared the poor, big-balled mammal’s life at the last moment. (If you think about it, this is true of the English, too: “I almost killed him.”)

Apparently, the way to express this is 殺しそうになった。

This is the other usage of そう, which describes the way something looks or appears. It’s often used with adjectives. You’re all probably familiar with these two:

うまい        うまそう        Looks/appears tasty.
おいしい     おいしそう      Looks/appears delicious.

So you can probably figure out what these mean:

危ない        危なそう
難しい        難しそう
暑い           暑そう

This pattern can be difficult to remember and difficult to say. I think the best way to think about it is to consider it an actual conjugation of the adjective, the Appear-ative tense if you will. If, for example, you learned this conjugation from the very beginning along with something like the past tense, wouldn’t it be easier to remember?

That would give us a small list like this:

Present             おいしい
Past                 おいしかった
Negative           おいしくない
Negative Past     おいしくなかった
Appear-ative      おいしそう

There would then be two things you need to remember about this conjugation. It differs from other conjugations in that to make it past tense, you must attach a copula – でしたor だった. The other is that it is a な-nominal – when you modify a noun with it, you must connect it to the noun with な, just as you would with words like 有名, 静か and 貧乏 (Look ‘em up!).

Consider the following:

うまそうなラーメン        tasty-looking ramen

暑そうな砂漠                hot-looking desert

難しそうな試験             difficult-looking test

When you have these in a sentence, you’ll find you won’t need hyphenated adjectives as much:

あのラーメン、うまそうだろう！    Damn that ramen looks tasty!

やばい。この試験、難しそう。        Crap. This test looks hard.

Okay, so that’s how adjectives work, but you can also use this tense with verbs:

食べる    食べそう     appear to eat
行く        行きそう    appear to go

Let’s check ALC and see if it has any example sentences for us:

あら、彼女、パーティーか何かに行きそうな格好しちゃって。
Whoa, she looks like she’s going to a party or something.

This is clearly a spoken sentence, and that’s important in this case, because it’s clear that the speaker is actually looking at this woman who is all hooched up – she is in a figure/appearance (格好、かっこう) that looks like she is going somewhere, specifically a “party or something” – and decided to vocalize surprise at the woman’s hooched-up-edness to the person standing next to her.

Back to the homework sentence. Let’s look at a verb chart for 殺す which means to kill.

Present                        殺す                Kill
Past                            殺した              Killed
Present Progressive        殺している        Is killing
Past Progressive            殺していた        Was killing
Desire                         殺したい           Want to kill
Potential                       殺せる             Can kill

Appear-ative                殺しそう            Looks like x is going to kill

殺しそうになった。

So, now we understand the first part of the sentence. It’s un-subjected in the Japanese, so it’s clearly “I.” But we also have ～になる, to become, in past tense form, so the sentence literally  means: “(I) became so that I looked like I was going to kill (the tanuki) (with my brand new car) (in the mountains between Nishiaizu and Kitakata).”

Not exactly the way we say things in English, but a very economical and accurate way of expressing the fact that I almost ran over (almost killed) a tanuki.

Robin was the closest with his guess, ‘A kid was being a little shit and you were "this close to killing him",’ as it correctly expressed the fact that I was close to killing something. So the beer goes to Robin.

Many people incorrectly answered using the Desire conjugation. Let it be known that I had no desire to kill the poor tanuki.