I recently read a good yarn about aliens invading the earth ("Footfall’).
I’d like to read some more alien invasion stories, but don’t know where to begin.
Sugestions?
War Of The Worlds by HG Wells
War of the Worlds, as pointed out, is the quintessential alien-invasion story. wells did it (almost) first, and did it right.
But Washington Irving beat him to it by decades. Read “The Conquest of the Moon” (1809) – Moon-men invade and conquer the earth. Using heat beams! I wonder if wells read this?
Another early invasion story wortn reading is Kurd Lasswitz’ Zwei Planete (Two Planets) is surprisingly good, was a major influence on Werner von Braum, Willy Ley, and Gritz Lang. It was only translated into English once, and then not completely. Surprisingly sophisticated, it came out the same time as War of the Worlds, but portrays Martians that are more sympatheic than the Earth people.
Of course, you have to read Robert Heinlein’s The Puppet Masters. Preferably the recently restored version. It reads like James Bond vs. Invasion of the Body Snatchers, but it predates both James Bond AND Invasion of the Body Snatchers. If you want, you can read Jack Finney’s IotBS if you want, but I find it disappointing.
Arthur C. Clarke’s Childhood’s End is considered a classic, but he’s written at least one humorous short story of the invasion of the Earth by aliens who direct their attention at getting — the account numbers of Swiss bank accounts.
Jack Chalker wrote an invasion story from the point of view of the invaders in Web of the Chozen. And he did a sort of brainwashing invasion story in Dancers in the Afterglow .
Check out this Wikipedia page on the topic:
I want to add my votes to those for War of the Worlds, and The Puppet Masters. (Though I haven’t read the restored version.)
I’ll add a few more fun ones: Here’s a recent alien invasion book that I enjoyed. For all that the invasion was 20 years before the action opens. This link to Course of Empire by Eric Flint and K.D. Wentworth goes to a free online version of the complete book, made available by the publisher, Baen Books.
Less simple is Harry Turtledove’s World War series, which begins with In the Balance: It posits an alien invasion beginning in 1943, at the height of WWII. Grand fun, but the first series is four books, the second three books, and there’s a final book, as well, so a total of eight volumes if you choose to follow the whole saga.
I’d like to suggest a slightly off-beat take on the alien invasion theme: “They Walked Like Men” by Clifford D. Simak.
The aliens are bent on taking over earth, all right, but they’re doing it by…well, buying it piecemeal, all nice and legal.
It is an older novel, but I really enjoyed it and you might, too.
“The Screwfly Solution” by Racoona Sheldon. Chilling.
Was that ever published under her real name? If not, look for James Tiptree, Jr.
Fredric Brown’s Martians Go Home is a unique humorous take.
I enjoyed Harry Turtledove’s “Worldwar” series, an alternate history yarn in which aliens invade right when World War Two is at its height in 1942.
AFAIK, it’s always published under the “Racoona Sheldon” pseudonym. It may be included in Tiptree anthologies, but it’s never been published under Sheldon’s real name. 
Other stories in the genre:
Fred Pohl’s “The [Day After the] Day the Martians Came” (The three words are generally dropped from the title, but I prefer the original).
“Punch,” also by Pohl.
“Men Without Bones” by Gerald Kersh
Battlefield Earth.
ow! stop hitting me!
If he’d ever freaking finish it, David Gerrold’s War Against the Chtorr series is interesting.
Wikipedia says that the 5th book should be out this year, but considering the first book came out in 1983 and the fourth book came out in 1993, I’m hoping the both the author and I live long enough to finish.
That’s the series I came in here to recommend… and, like you, I’m afraid the series will never be finished. Dammit.
Lunch! 
A number of Heinlein’s novels have been re-issued recently in the original versions, that is, in the version as Heinlein submitted it to his editors, who usually requested cuts.
In most cases, the cut version reads better, but the uncut version includes more Heinlein “flavor”, which is good in its own right. Stranger in a Strange Land is an example.
Puppet Masters, however, was severely cut for content. The restored version is almost a different novel. Red Planet was also cut for content, although quite a bit less seriously. Reading both in the original versions is highly recommended.
I think that’s a misleading statement. They didn’t cut that much out of Puppet Masters. The uncut version is somewhat more risque than your typical early-fifties novel, and the description of life in the Red Zone is a more disturbing, but all of that is “more of the same”. The implications for the same situation are in the cut novel that I first read back in my teens (One of the first SF novels I ever read).
Breath: Don’t hold it.
Depending on what parts of Footfall the OP found interesting, I’d provisionally recommend John Ringo’s Posleen War series. Start with A Hymn Before Dying. If that’s to your taste, continue with Gust Front and When The Devil Dances. After that it’s up to you.
The first book in John Ringo’s Posleen books (The Legacy of the Aldenata, officially) is actually titled A Hymn Before Battle. The link goes to the Free Library HTML version of the book. Get a taste of it before buying anything.
I have very mixed feelings about the books in the Posleen War. A lot of the politicizing of the military rings very true to me. And the minor characters are awesome. The aliens are interesting, and dangerous in ways that most invasion aliens aren’t. But I can’t stand the main character. He just reads like a bad Mary Sue fanfiction character to me. YMMV, of course.
I’ve really enjoyed the side books for the milieu that Ringo has written with Thom Kratman, though. Take a look at it, you might like it. And you might not.
Die Wacht am Rhein alone made the series for me.
I’m a former squid. I prefered Yellow Eyes. I just liked the confirmation about what the ships are really thinking, between Daisy Mae and Sally. 
An alien invasion story (but not an invasion of Earth) is David Brin’s The Uplift War - aliens invade a human/chimp colony world as part of the larger Uplift Saga of books.
Also, the Jijo trilogy of the same (also called the Second Upift Trilogy) - aliens (some of whom are human and other Earthlings) invade another, outlaw, mixed colony world(some of whom are human and chimp) - Brightness Reef, Heaven’s Reach and Infinity’s Shore.
Brin writes some good aliens. I especially liked the Traeki/Jophur.