You can't download the old Google Maps app separately in the App Store. Rumors are flying back and forth about whether Google is about to release it as a standalone app, but even if they're true (which it looks like they're not, at least for the time being), Apple could still refuse to let it through the way it did with Google Voice.
So what are your alternatives now? A lot of people have pointed out that you can still access Google Maps via the iPhone's built-in browser. That's true, but it's a pain, and you don't get live GPS location that way, so you can't use it to walk around and see what's around you. Native apps are still better.
Here're the best free mapping and navigation apps available.
Bing 3.03 (Free)
Bing is more of a general search app than the others, but it also delivers solid maps and navigation. It has a comprehensive POI database, and delivers walking, transit, and driving directions (at least without voice prompts, like the old Google Maps app). It also includes traffic conditions, movie showtimes, and robust Facebook integration.
Hopstop for iPhone 2.0 (Free)
The public transit-focused HopStop gives you GPS-enabled directions, transit schedules, and maps that include subway and bus stops for 62 cities across the U.S. You can set it to prefer a certain kind of public transportation, such as to take the subway whenever possible. It also estimates taxi travel times and cost and lets you call for one, and it can deliver biking directions in four major cities as well as wheelchair accessible and stroller-friendly routes.
MapQuest 3.0.3 (Free)
We didn't like MapQuest's driving directions in our review, as it felt grafted on and in some cases was vague enough to be dangerous. But on foot it's excellent, and is a great option if you're looking for a pure Google Maps replacement with a moving, overhead 2D view. The latest version features live traffic cameras and gas prices in addition to walking and driving directions.
TeleNav Scout 1.2.1 (Free)
TeleNav has a variety of iOS apps already out there, but Scout, its latest one, is the most compelling. It offers free visual directions, point-of-interest search, and a nicely laid out dashboard UI with traffic, weather, and commuting times. It also accepts voice input for navigation commands. A $9.99 per year in-app purchase adds voice prompt-based navigation (for while driving), offline maps that work without cell coverage, automatic traffic-based rerouting, speed and camera trap alerts, and lane assistance.
Waze 3.2.2 (Free)
Waze (pictured right) delivers free, crowd-sourced GPS navigation with strong social networking and community tie-ins that deliver unusually accurate, real-time ETAs and optimized routes. It also alerts you to upcoming police speed traps, and with proper voice-guided navigation, it's a great stand-in for a portable navigation device, even though it doesn't always deliver the most sensible routes overall. It's getting better and better at that, though—by design.