Japanese-English Dictionary Software (also English-Japanese)
Sanseido.net offers an excellent concise Japanese-to-Japanese dictionary.
Jim Breen's WWWJDIC is a free, community built online dictionary. The definitions are not nearly as thorough as professionally compiled dictionaries but it's a good way to get the gist of a word if you need help in English.
Electronic Dictionaries (電子辞書）
I really love my Canon Ex-word 6900, but I recommend it only for advanced learners.
Nintendo DS Dictionary Software
I know the Nintendo DS has a reputation as a toy, but the dictionary software uses the Genius Japanese-English dictionaries-- which is what most of the other denshi jisho use as well. But because the Nintendo DS has a touch screen, you can write the kanji you want to look up, rather than the reading, so if you're totally unsure of the reading it's an easier way to check definitions. And perhaps best of all, even if you don't already own a DS, you can buy a brand new DS and the dictionary software for less than $180, which is far cheaper than most of the dedicated denshi jisho.
Quick and dirty English Guide to getting started with the dictionary.
My favorite dictionary is the Mac OS Leopard dictionary (see below). However, for those of you who use another OS, I really like StarDict, which is perhaps the most widely used dictionary program in the world. StarDict has a crappy interface, and all of the dictionaries are bundled separately- but they are a few dozen for Japanese alone (there are StarDict dictionaries for all of the languages you know, and for many that you may have never heard of). As such, I think in this case the tradeoffs are worth it.
Also, StarDict allows wildcard queries, meaning that, for example, if you know the second kanji but not the first in any given word, then you can search for "*kanji" and it will display all possible matches. I find this really handy when reading.
StarDict runs on Linux, Windows, and the Mac. In other words, if you have a computer, you can probably run it.
All of the StarDict dictionaries are openly available; these are free dictionaries, but you will sometimes find them bundled by unscrupulous commericial vendors. But there's no need to pay; just download StarDict!
The Japanese dictionaries can be found here.
The Mac OS X Leopard Dictionary
If you're a Mac user, and you use Mac OS 10.5 or later, you're in luck-- the new dictionary application has the Progressive Japanese-English dictionaries built-in. This is a fairly common electronic dictionary that has many examples in context to make your life easier.
Japanese and Japanese-English are not, however, searchable by default. To use Japanese, open Dictionary (in the Applications folder), choose "Dictionary" from the Apple menu, select "Preferences", and then check "Japanese-English" (and pure Japanese if you want).
The great advantage of this setup is that you can look up words you don't know (in the dictionary explanations) simply by clicking them with the mouse.