The story, written early in Lovecraft's career, is one of his lesser efforts, but one that his fans generally like. My reaction was pretty bland the first time I read it, but more recently I've come to appreciate it much more. I'll summarize it for you, so those wishing to read the story first should skip the next two paragraphs, but you won't get much out of this entry if you do.
The titular Terrible Old Man is an old sea captain, living in a crumbling house on the outskirts of an ancient, New England fishing village called Kingsport. He pays all his debts in unusual gold coins, and people brave enough to have peered in his windows report that the house is full of glass jars with pendulums suspended inside. He spends his days talking to the jars, and the pendulums swing as if in answer, but of course, that's ridiculous; this is all heresay.
Three petty criminals with offensively ethnic names enter our story and make plans to rob the old man on the grounds that he's 1) probably too weak to put up a fight, and 2) obviously crazier 'n a loon. Two of them go up to the house while the third keeps the getaway car ready to go. When they don't come back, the third goes up to the house and peeks in a window. There are two new jars on the table. He turns to see the Terrible Old Man advancing toward him, down the garden path, with glowing, yellow eyes.
That's it -- the whole story. As I said, I was unimpressed at first, but subsequent readings have given me an appreciation of the economy of the prose and the narrative. Yes, it's simple, but it's also creepy and very strange. My initial reaction was that the ending is a cop out, but now that I've had a little time to explore its possibilities, I find myself more affected than I had originally been. At this stage in his career, HPL was aping the works of Edgar Allan Poe and (as in this case) Lord Dunsany. The setting, Kingsport, was inspired by a visit to Marbelehead, MA, and is the backdrop for a few of HPL's early Dunsanian fantasy tales in which he tries to capture a sense of wonder rather than of the macabre. They are my favorite of his early works. Also worth mentioning, The Terrible Old Man makes a much more benevolent appearance in a longer, more complicated story called "The Strange, High House in the Mist", which is a favorite of mine, but I don't see how you could adapt it for screen.
A quick Youtube search will bring up several low- (or no-) budget adaptations of "The Terrible Old Man". Some are animated, some are live-action. Some take gross liberties with the source material, while others play it very safe. I have to confess, I prefer my Lovecraft adaptations to stick to their source, but of all the versions of "The Terrible Old Man", my very favorite is a short called Prey which skips the jars and updates the setting from quaint and picturesque New England to a more modern, inner city setting. I can't really explain it; the heart of the story is retained, but I like it because it is constructed of such different materials. Like the original, it has significant flaws, but also like the original, it's so short that the flaws are easily overlooked, and it continues to impress me with subsequent viewings.
You can read the original story here, and its sequel here.
Samples of the many adaptations of the story: animated, and CGI.
And of course, Prey can be seen on Youtube.