Adjectives like 好き can only be used on nouns (ケーキが好き, 好きな猫). If you want to use it on a verb (like "look"), you need to turn this verb into a noun first ("the act of looking"). This is what the の does; it's called a normalizer.
So, a very literal translation of your sentence would be: as for me, the act of looking at pictures is likeable.
I have a terrible habit of writing half a post, getting distracted by a different browser tab, and then coming back to find somebody else has already responded with basically what I was going to say, so it makes a nice change.
It serves the same purpose that "-ing" sometimes serves in English; it nominalizes (makes into a noun) a verb.
The presence or absence of the の would have the same effect on the ears of a Japanese native speaker as would the difference between:
1. I like looking at pictures
2. I like look at pictures
on the ears of a native speaker of English. Yes, it is intelligible even with the error. But the omission is jarring and if you have to hear it over and over it gets annoying. Not as unpleasant as having a cheese grater vigorously rubbed over your ears, but close.