Okay, it appears to me that each of us is having slightly different problems; here's mine, maybe it can help someone. I beat my head against the desk for a week on this.
Anyway, Droid X, rooted, no 3rd-party ROMs. Home LAN is D-Link DIR-655, all devices static IP. Tried the "g only" trick, DHCP instead of static, set sleep to Never, all the stuff mentioned here & elsewhere, but I got the same symptoms a lot of others got i.e. connecting, obtaining IP address, disconnect, lather-rinse-repeat, no joy. Went to the doctor's office and while waiting, just for $#!+$ and grins I tried getting on their free public WiFi and it connected. It appeared to me that it was just an issue with static IP (though at first it wouldn't connect on DHCP either). I got ifconfig from the Market (I'm a Linux guy) and while there I saw something called WiFi Static; it's for saving various configs for different networks so you can bounce back and forth between work, home, Starbuck's, whatever. I figured what the hell, the worst that can happen is nothing. I got it and set up my static IP profile; restarted WiFi and I'll be damned but it worked, web, LAN and everything. I don't need to half-ass the security on my router, it doesn't drop out, nothing, it Just Works. ***This is not spam, I'm just saying what I did.***
Again, I'm sure there are different things going on with different phones and I agree, the WiFi stack is broken bigtime (mine was one that would disconnect every half hour with 2.1) but the way it was acting before and the particular app that I got tells me at least some of the problem is IP-related. I didn't write the app and I don't know who did but I'll find out after I send this and look into a donation; it has to be worth at least the gas I'd burn driving to the Verizon store and dealing with the halfwits there. Everyone who is still having problems, look into how (or if) the phone is trying to pull an IP address whether it should be or not.