While the fast zombie movies are technically in the same genre, I think they are not the same as shambling zombie movies.
Zombie movie traits:
1. Zombies, or something similar (28 Days)
2. Survivors:
a. Lucky, found someone to help them
b. Average person turned onto an extaordinary person due to events
c. Bad ass
d. Leader
3. Stronghold. Not necessarily a good one, but it encloses the survivors for interpersonal relationships.
With fast zombies, a lot of the tension between survivors is taken away.
To jrderego, I only remember the remake of Invasion when they tried to get away in a helicopter at the end. I guess I just hold the original in such high regard that the rest can't compare. The end of Invasion of the Body Snatchers is one of the all-time best!
As far as scary movies go, Phantasm did it for me. Of course, I was 5 when I saw it the first time...
Phantasm was awesome, I saw that for the first time on UHF TV when I was 9 or 10 and it scared me senseless.
There are so many invasion remakes it's hard to catalog them all.
There's the Don Siegel original
The 1978 version directed by Phil Kaufman, which lost the whole communist paranoia angle
The 1992 version directed by Abel Ferrara set on an army base and featuring teenage leads
The 2007 version with Daniel Craig and Nicole Kidman which is closer to the 1978 version than any of the others
A couple of other films that explored similar territory with varying degrees of success are:
It Conquered the World! (Roger Corman cheapo featuring a giant space celery as the monster).
Zontar: the thing from Venus (An ever more cheapo remake of It Conquered the World, shot for TV by Larry Buchanan).
The Puppet Masters, based on Heinlein's book of the same name.
As for the fast vs. shambling argument...
The point of Zombies, at least to me, isn't that they are faster or stronger than non-zombies, it's that there are an exponentially increasing number of them, and while you might be faster than they are, you'll have to stop and they won't. If you end up sheltered in a place the eventual sheer numbers of them outside will make it impossible to stay secure, or alive (once supplies run out).
I am actually struggling with the novel based around the Pleasant Hollow stories at the moment so it's easy for me to get sidetracked with Zombie stuff - that said, in my book and the stories, the zombies shamble. The idea being that even though decomposition is slowed in the undead, it's still occurring and that their muscle tissue dissolves just like the rest of them does. So while they might be almost walking normally when first coming out of rigor mortis and starting to move, within a couple of days they are are dragging a leg, or crawling on just arms, all bloated and nasty, until they pop and finish rotting. The stories are fun because I've set them to be at ambient temperature, so the winter isn't all that bad for the survivors as the zombies are frozen solid out in the wastelands. But in the spring and summer it gets increasingly hard to avoid them, while the zombies themselves get a much shorted undead life span due to the heat.