The difference is very slight, and is one of aspect. When you use the infinitive after "like" you are probably not performing the action, but are rather talking about the action in the abstract.
When you say "I like" plus the gerund, you are probably engaged in the activity as you speak.
This is not a clear-cut distinction, but it's often the case.
In The Grammar Book (Heinle & Heinle, 1999) Celce-Murcia and Larsen-Freeman state:
"Some degree of correlation exists between the choice of infinitives with events that are "hypothetical, future, unfulfilled" and the choice of gerunds with events that are "real, vivid, fulfilled," a fact that was first pointed out by Bolinger (1968)." (p. 648)
You'll find a related, but slightly different explanation on the board dated November 30, 2004 under the topic 'Like -ing vs. like to." It's currently on p. 31.
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