Ask any Web developer to name a few browsers and you'll get basically the same list: IE, FireFox, Safari, Opera and a few others. Ask them to name a few mobile browsers and the answers will vary considerably. If you want to be able to give a fairly complete answer to such a question, here's a short list...

• Android - strictly the name of Google's Linux-based mobile OS, the built-in browser is based on WebKit. For added functionality, a popular free touch-based UI layer for the browser is Steel.
• Kindle - a monochrome mobile e-book reader from Amazon, it comes with an experimental Web browser capable of basic text layouts. The UA reports the browser to be NetFront/3.3.
• BlackBerry - the browser from RIM embedded in their BlackBerry devices.
• Blazer - a free NetFront-derived browser found on Palm handhelds.
• Bolt - a free independent Java-based mobile browser built on ThunderHawk from Bitstream, for Palm, BlackBerry and Windows Mobile 6.
• * Deepfish - zooming browser from Microsoft that was canned in 2008. The architecture was similar to Opera Mini.
• Fennec - the successor to Minimo, this is the mobile version of FireFox.
• IbisBrowser - popular Japanese i-mode mobile browser.
• Internet Explorer Mobile - IE for mobile, found on all Windows Mobile platforms.
• Iris Browser - WebKit-based browser for Windows Mobile.
• * JOCA - free Java-ME browser that uses a Web proxy for page compression.
• Konqueror Embedded - self-contained embedded version of the well-known Linux desktop browser, based on the KHTML engine (the origin of WebKit).
• MicroB - Nokia's maemo browser on the N8xx and similar devices, based on the Gecko rendering engine.
• Minimo (see Fennec) - the Mini Mozilla, a scaled-down version of FireFox. The project was closed in 2008.
• Myriad - previously the OpenWave browser (redeveloped with WebKit), renamed when acquired by Myriad Group (France) from OpenWave's mobile client division in 2008.
• NetFront - embedded browser from Access Co. Ltd (Japan) supporting cHTML/i-mode and XHTML-Basic.
• Obigo Q7 - an S60 and WinMob browser from the Hong Kong based company.
• * Opera Mini - a popular distributed mobile browser from Opera that transforms the Web via a proxy server.
• Opera Mobile - a full mobile Web browser for Windows Mobile, UIQ and S60 platforms using Opera's Presto layout engine.
• OpenWave (now Myriad) - Widely used mobile browser that incorporated some features from Magic4 (the UK company acquired in 2004). Supported HDML before the introduction of WML. At one point, half of all mobile browsers were OpenWave.
• Pixo Internet Microbrowser - a component of the embedded OS originally in the Apple iPod. Long since confined to history.
• S40 - Nokia's embedded software platform containing a WebKit-based HTML browser.
• S60 - Nokia offers a WebKit-based browser for its S60 mobile platforms.
• MobileSafari - Apple's KHTML/WebKit-based browser for the iPhone and iPod platforms.
• * Skyfire - distributed mobile browser for Windows Mobile. The proxy server uses the Gecko engine to render normal Web pages before being sliced into smaller images for the client.
• Steel - a fork of the Android browser.
• * Teashark - distributed MIDP 2.0 browser with a WebKit-based renderer in the proxy server.
• * ThunderHawk - distributed MIDP 2.0 and Windows Mobile browser from Bitstream, with zoom-in/out features.
• * UCWEB - the distributed "You Can Web" browser is very popular in China and comes in both Java and native (Symbian, Windows Mobile) versions.
• Unwired Planet (UP) Browser - later to become OpenWave and subsequently to be acquired by Myriad. Some say this was the original mobile browser.
• * uZard Web - a distributed browser from Korea that runs on several platforms. It presents full desktop pages in miniature.
• WinWAP - an old WAP browser for Windows Mobile, now also supports WAP 2.0, HTML etc.

This is not an exhaustive list. I am leaving out certain automotive browsers (which are mobile, but not carried by people) and most of the non-portable embedded browsers (such as Opera's embedded browser for Nintendo's Wii games console). I'm also leaving out services like Skweezer and Google Mobile as these don't have a client application, but instead rely on whatever browser already exists on the device. Also out are e-book readers with basic Web facilities such as reading RSS feeds, though I've included the Kindle as its browser is just about good enough to use.

Browsers marked * are distributed browsers that rely on an intermediate server to do some/all of the page transformation to adapt to the constrained mobile environments.