What's the difference between "I look forward to" and "I'm looking forward to"?

I look forward to seeing you means I await eagerly to see you.

I am looking forward means I am looking at the area in front of me.

Look forward to is a phrasal verb that means to await eagerly. It can be used in any tense. Examples:

• I look forward to meeting you tonight.
• He looks forward to graduating this year.
• We dare not cancel the trip to Banff. The kids have been looking forward to this for ages!
• Both were looking forward to spending a wonderful evening together, but the weather cruelly disrupted their plans.
• I can't believe they're actually looking forward to vacationing with us for three weeks. This house is super boring!
• Even though he knew it would be difficult and unpleasant, he still looked forward to having a heart-to-heart conversation with her.

The sentence

I'm looking forward

cannot be interpreted to mean eagerly awaiting, as it would have to be followed by to_.

Thus, it can only mean one thing:

I am directing my gaze (or view) forward

where forward is an adverb. This usage, however, is not common in regular conversation, except in very few circumstances. Nevertheless, it is definitely acceptable to say:

I'm looking forward to it!

to indicate that one is eagerly awaiting an event.

Look forward to something or look forward to doing something means "to excited and pleased about something that is going to happen"

I'm really looking forward to our vacation.

But "I Look forward" can meaning with trivial differences according to the context. For example it can mean I'm looking to the area in front of my eyes.

Hmm, okay, a totally non-grammatical (probably, and thus very likely totally wrong) answer by an avowed non-grammarian (who nevertheless described and describes himself as a grammar-nazi at times):

"I'm looking forward to" means I'm doing it right now, this very instance, like in Elendil's example of being on the phone with a friend; I disagree that it's about formal vs non-formal, it's due to being on the phone with that friend in that moment, so of course you'd be looking forward to meeting said friend at that very moment.

"I look forward" means looking forward in a general sense; like, you'd not think about meeting your friend every second of the day, but the anticipation would be in the back of your mind all the time.

That's my take, and I'm sticking to it. ;-)

Assuming you mean "I look forward to ..." and "I'm looking forward to ...", they are essentially the same thing. However, there is a slight difference. the -ing on "looking" is a present participle.

So if we consider "look forward to" to mean "anxiously await", then we can rewrite the phrase as:

"I anxiously await your visit", vs "I am Anxiously awaiting your visit".

So in this case, "look" and "await" are the verb, and "forward" and "anxiously" are the adverbs.

So it's sort of a active/passive thing. "I am" versus "I". You would not say "I looking forward to" or "I am look forward to". It is effectively the same thing as "I look" vs "I am looking". for example "I look good" and "I am looking good".

My take:
'I look forward to hearing from you' means you expect something to happen.
'I am looking forward to hearing from you' means you are now excited about a future event.
Both cases can be used when you expect a reply from a person you email. Still, the connotation is different.

Another example:
'I see an accident happening' means you expect an accident to happen.
'I am seeing an accident happening' means you now see an accident happening.

Source: http://theicingonyourenglish.com/i-look-forward-to-vs-im-looking-forward-to/

Progressive forms can make requests, questions and statements less direct. (They sound less definite than simple forms, because they suggest something temporary and incomplete, e.g. "I'm looking" forward to seeing you again. - - Practical English Usage by M. Swan,