I wouldn't go so far as to say Wave will fail, but it's not going to be the amazing success that Google seems to expect. Gmail was incredible because until it came out, no one thought to use AJAX to make web mail act like a desktop client. It instantly obsoleted every other web mail package. Every now and then I check in on Hotmail and Yahoo mail and they *still* lag far behind Gmail; I don't get it.
Email itself was well-accepted because at the time it was released there was no way to send messages to people cheaply and reliably; fax machines were for the rich, long-distance phone calls were expensive. It was also very simple; spend an hour reading the RFC and you could send an email from any machine that could telnet to an SMTP server. Wave is somewhat complicated to understand at first, and the programming API seems to join Java, JSON, XML, and maybe some form of REST in a way that is going to flummox anyone that doesn't want to devote full-time attention to writing things to work with Wave. I can check my Gmail from my Blackberry, but I'm going to have to wait until Google writes an app for Wave because there's no way the Blackberry browser will handle the HTML/CSS/JavaScript features that Wave requires. That's ignoring the fact that Wave practically requires a keyboard and mouse.
Wave doesn't really introduce anything new; it tries to improve several existing technologies but doesn't sparkle. I don't see any earth-shattering improvements like Gmail had. IM can do what Wave does, but isn't designed for multiple users or document generation. You won't stop using IM for things like "Hey do you want to see a movie at 8?" because Wave will take much longer to set up the conversation and you'll have to decide if you want it archived or cluttering up your inbox forever. IRC chat rooms can be used to do what Wave does, but aren't as structured. You won't stop using IRC for chat because Wave isn't as robust and most people's IRC chats aren't worthy of "archive forever". Email can do what Wave does, but it's not as convenient. You won't stop using email because you can send and receive email from a Speak 'n' Spell and it's fast; you also don't need document collaboration and threaded discussion to tell your friend you'll be 10 minutes late. Word with comment-tracking features can do what Wave does, but multi-person collaboration is difficult. You won't uninstall Word because you'll still need fancy page formatting features and there are some documents that people cannot legally allow Google to save for them. Phones can do what Wave does, but time zones and phone charges make it impractical. You won't throw away your phone because you can speak faster than you can type, and if you're calling to make sure the baby's OK you don't want to wait an hour for the babysitter to remember to check Wave. The common thread here is that Wave takes a very complicated scenario that all of these technologies fail at and does it well. Unfortunately for Wave, 90% of people only care about the simple scenarios these technologies excel at.
It's fun for some things. I'm participating in one that's spading an unknown game mechanic in Kingdom of Loathing. It's a great idea and would work, except Wave craps out as soon as we get about 100 posts into the Wave and the Google spreadsheet crashes roughly every 300 edits. We could have planned our Thanksgiving potluck using Wave and saved some agonizing phone tag. I write a lot of programming tutorials and Wave would be nice for getting feedback before I submit them. Yet while I use Gmail multiple times per day, I can only see myself using Wave a few weeks out of the year.
The closed beta is the worst possible way to release a product like Wave. You need to collaborate on something with 10 or 15 people to really see it shine. When I got my invite, I had 1 contact: the random person on Something Awful that sent me an invite. Now I've got 4 contacts who all logged on, posted "hooray thanks for the invite" and I never saw them again. It'd have been a lot easier to get what it was if, say, Wave launched on a Wednesday night and Google invited all members to a Wave discussing and analyzing the airing episode of MythBusters. Or if they launched it on the night of a big Obama speech and invited everyone to a Wave discussing it.
So yeah, I'm a big nerd that's spent way too much time analyzing Wave. It's because I follow a lot of tech nerds and they wouldn't shut up about how awesome Wave was until more people started using it and we realized that it wasn't really that good. It's not the best thing since sliced bread, it's bread with peanut butter pre-spread on it: perfect for making peanut butter sandwiches but you're SOL if you want cheese toast.