Is it "Look forward to seeing you" or "Looking forward..."?

Generally, I’d say, “Looking forward to seeing you…”

In essence, you’re just leaving off the subject of the sentence. So you’re basically signing an email as “I look forward to seeing you,” or as “I’m looking forward to seeing you.” In my opinion, the latter sounds better.

Technically, grammatically, both could work.

I look forward to seeing you!

We’re looking forward to seeing you!

Either could work. I just keep in mind the subject I’m implying if I leave it off (I/we).

@SpatzieLover: But “looking” could work if the person is leaving off “I am.”

U R correct.
I don’t use either anymore.
I’m trying not to lie (especially to the sis-in-laws) ;)

“I look” is noun- verb. “Looking” is gerund (verb derivation that functions as a noun when used alone). “Having a wonderful time.” “Do you mind my asking you?” “Greetings. Uncle Sam wants you.” “Seeing is believing.”

Actually, “looking” in this case is simply a participle, I believe. It does not function as a noun in the sentence, “I am looking forward…” It still behaves as a verb. To answer the original question, as someone already pointed out, both are grammatically correct with the assumption that you drop the subject of the sentence (+linking verb).

I like “Smell you later”.

@astro, me too.

This one too:

Things to see, people to do.

It’s a question of tense aspect. To make the difference between the two clear, we can extend both fragments to the full statements that they imply.

“I look forward to seeing you.”
“I am looking forward to seeing you.”

In this case Ibrooker is more correct than gail in the role of “looking.” It is a participle that acts as part of a verb (the other part of the verb “am” is implied) and not a noun that stands on its own.

The distinction between these two sentences is subtle. They’re both present tense, but one is in the simple present, whereas one is in the continuous present. You can probably see how they get their names—the former implies a general state of being, like a habit whereas the latter implies a state of being specifically continuing at this moment. It would be the same as the distinction between the sentences “I like ice cream.” and “I am liking ice cream.” In this case, one appears to be a sort of general statement about my feelings towards ice cream—which presumably are pretty consistent. The other is a statement regarding how I feel about ice cream right now—presumably because I have some and am eating it.

After some reflection, I think I’d probably use the latter. After all, it is not a general state of being that I look forward to seeing a particular person (unless this person is a romantic interest, I suppose: “I constantly look forward to seeing you!”) but rather something I am feeling right at this moment. Right now I am looking forward to seeing you. But in all likelihood, that’s not always how I feel.

But, again, the distinction is subtle, and I suspect that even the most obsessive linguists would not notice if you used the other form.

That was interesting, lapilofu. How would you parse “Seeing is believing”?

Or let’s go back to “looking.” “Here’s looking at you, kid.” Or “Looking forward to clearing this up” w/o the “I am.”

And would you really say, “I am liking ice cream”? That seems very awkward in English. “I like ice cream.” “I like the ice cream that I am now eating.”

However, the last time I had anesthesia, when I woke up, I said, “Help. I am seeing double.”

Interesting in a nit-picky way….haunted by sentence fragments tonight. I am sorry.

In the case of “Seeing is believing” your explanation of a gerund holds, because “seeing” is clearly the subject of the sentence—otherwise it could not take a verb. Seeing is believing. “Is” is the verb of that sentence.

In “Here’s looking at you, kid” I think that “looking” is also a gerund—in this case the object of the sentence. Though the grammar of that sentence is so confused that I struggled to make that decision. Here is how I would interpret it:

Here (subject) is (verb) looking (object).

So in this case, “looking” is a noun.

However in “Looking forward to clearing this up,” looking could not be a noun. It does not take a verb, nor is it the object of one. Therefore I would say that this is a sentence fragment with an implied subject and verb “I am” before it.

And you are absolutely right that I wouldn’t say, “I am liking ice cream.” I knew it was awkward when I wrote it, but I just couldn’t think of a better example—and I didn’t want to add more words to the sentence that might confuse the distinction. Here are some examples that maybe provide clarity. (Not that you requested clarity, Gail—you seem to understand my explanation—but for anyone else who was maybe confused by an awkward example.)

“I see dead people.” versus “I am seeing dead people.”
“We eat meat.” versus “We are eating meat.”
“You train dogs.” versus “You are training dogs.”
“She sells seashells.” versus “She is selling seashells.”

Wikipedia has a few good tests to distinguish gerunds from present-participles but, by their own admission, none of them are perfect. And they’re designed for complete sentences, which makes it slightly trickier if you’re not assuming a full sentence.