A simulator is software appearing on a computer that acts like the target environment. A browser that is the same size and the same official standards as the target browser, but not the actual code the target device is running. An emulator is running the actual code, so from a technical perspective you can have confidence in the fidelity.
Web-Based
dotMobi Online Emulator - focus on common phones; likely to be a simulator not emulator. Run by YoSpace.
Opera Mini Simulator - Opera's J2ME browser.
Bolt Browser Simulator - Intended to sell the product, but useful to check how things might work on a small-screen, scroll-and-select browser.
Device Anywhere - Actually a new class, a virtualization system. Actual hardware is disassembled, things are soldered to it, and it's strapped to cabinets. You get to press buttons and it goes over a real network, and gives you the screen output. Free trials available with some developer programs, otherwise a fee service. But useful.
Applications
[http://www.forum.nokia.com/info/sw.nokia.com/id/db2c69a2-4066-46ff-81c4-caac8872a7c5/NMB40_install.zip.html Nokia Browser Simulator] - generic Nokia phone and gateway
[http://developer.openwave.com/dvl/member/downloadManager.htm?softwareId=23 Openwave Phone Simulator] - Openwave's simulator (probably actually an emulator)
[http://www.blackberry.com/developers/downloads/simulators/index.shtml BlackBerry Simulator] - multiple different BlackBerry emulators
[http://www.yospace.com/spedemo.html| Yospace SmartPhone Emulator] - displays multiple phone instances at the same time but may not have the best fidelity to actual devices
[http://www.genuitec.com/mobile/ iPhone/Pre Emulator] - Windows only desktop emulator, emulates both iPhone and Pre.
[http://developer.palm.com/index.php?option=com_content&view=article&id=1883&Itemid=56 Palm Project Ares] - Full web development environment for WebOS in the browser.
Prototyping / Wireframing
[http://www.zambetti.com/projects/liveview/ iPhone screen projector] - "tethers" with your mac to display content from your desktop on your iPhone. Requires a free iPhone app.
[http://sourceforge.net/projects/iphoneprototype/ iPhoneprototype] - Firefox plugin for iPhone mockups.
Full Design Suites
[http://www.g5e.com/games/MIDS MIDS] - flow charts, navigation, wireframes, rendering, and even a physical test device