Using "Special Characters" in Lion or "Character Viewer" in Snow Leopard (instead of the greedily overpriced PopChar) does NOT require any prior setup, and neither needs to be enabled in the Language & Text System Preferences. Both features are automatically accessible right out of the box in most text-capable applications — except Microsoft Word (the dicks) and a few others — RIGHT FROM THEIR MENU BAR: JUST CLICK THE LAST SELECTION (usually) IN THE EDIT MENU. It's that simple.

Even simpler, just enter COMMAND-OPTION-T, but only in programs that allow access to Special Character/Character Viewer from the Edit menu (so not in M$ Word), and only when you have a text-enterable window open (so it'll work in Safari when a text box is open, but not when viewing a normal webpage — you must be in text input mode). Cool, huh?

However, if you want to have the "Keyboard & Character Viewer" icon (which, bizarrely, does not reflect the Lion name change to "Special Characters") in the menu bar at all times — even though it does not affect any easier or faster access than simply using the Edit ➔ Special Characters/Character Viewer method (though it does give you a way of using Special Characters/Character Viewer with M$ Word!) — then use Bosskev's excellent instructions below.

In October of 2008, I left a glowing review of PopChar here on MacUpdate, even calling it a "must have" tool. While true at the time, and while PopChar probably continues to be an excellent utility, I must say I have long since moved on and no longer use nor pay for PopChar.

Character Viewer from Apple, already included on every contemporary Mac, does everything I used to do with PopChar, just as easily and just as well. The only trick is you need to know how to FIND Character Viewer.

Go to System Preferences > Language & Text > Input Sources, and then check two boxes: "Keyboard & Character Viewer", and "Show input menu in menu bar". Now look in the Menu Bar at the top of the screen, over on the far right side. You'll see a (very strange) little icon, sort of like a box with an asterisk on it. Click there, and then choose "Show Character Viewer". Done.

PopChar may or may not have additional functionality beyond how I use Character Viewer. But PopChar is just too unrealistic in today's global economy about its pricing. When I can buy an entire operating system such as Lion for $30 (and, furthermore, am authorized to install it on several systems), a one-trick pony like PopChar, currently selling for about $40, needs to seriously re-evaluate its pricing and licensing structure.

I’m a Geography professor and the head of a political public relations consultancy that serves mostly foreign governments of Turkic nations, so I use many unusual text characters in my daily work. After years of frustration, I got very tired of the complex and time consuming process of accessing the dozen or so characters that exist in the Turkish alphabet but not in English. So I bought PopChar two years ago, and I’m more or less satisfied with it. However, I feel that its developer overpriced PopChar by at least a factor of 2, and his upgrade policies are shamelessly greedy. Nevertheless, I bought it because I was desperate.

However, after buying PopChar, I discovered that OS X has its own utility for entering unusual characters that’s only slightly less convenient than PopChar — the Character Viewer (formerly called Character Palette). Anyone who’s thinking of forking out $37 for PopChar should know that the FREE Character Viewer that’s built into OS 10.4 through 10.6 does the same things in much the same ways as PopChar. It’s just summoned in a slightly less efficient way, and that’s PopChar’s only real advantage over Character Viewer, but it’s unquestionably NOT worth $37. Had I known about the Character Viewer before I bought PopChar, I would never have done so because it’s ridiculous price far outweighs the teeny tiny efficiency it provides vis-à-vis Character Viewer.

To use Character Viewer to input unusual characters in nearly all applications except Microsoft Word, Excel and PowerPoint 2011 but including Microsoft Outlook 2011, just click the ‘Edit’ menu and select ’Special Characters’ from the drop-down menu (or use the Option-Command-T combination). That will summon the Character Viewer interface, which is very similar to the PopChar window. If you frequently use a certain unusual character(s) and want it to be readily accessible, just find the character(s) in Character Viewer and add it(them) to its Favorites pane. Then, every time you use Character Viewer your favorite character(s) will appear front and center for easy 1-click entering into whatever text you’re writing. If you click the green button in the top-left corner of the Viewer, it will minimize to a very small, square window that you can place wherever you want to even more easily call it into service.

If you're working with multilingual texts, say diverse diacritics or just Romance and Germanic languages:
Have a look at the U.S Academic keyboard layout:

http://www.unibuc.ro/en/cd_sorpaliga_en

It's not perfect for my purposes, but pretty close.
Includes Hebrew, Greek, Cyrillic, Phonetic, Maori (ā) etc. etc.

My best friend for surviving massively multilingual linguistic projects. Including a lot of diacritics for all needs.

[bumped up from a comment myself]

I like Ergonis and their products, but even the recent 5-star reviews -from people who have never reviewed anything- can't make this look like an attractive upgrade.

I'm staying with version 4.

@RANDOM NUMBER GENERATOR,
Although their upgrade policy used to be very attractive, upgrades may not be free for 2 years anymore:
"If you purchase an upgrade now, all minor upgrades of PopChar X 5 are included for free in the one-time upgrade fee of only EUR 14.99 (single license)."

Great company, great products, excellent customer support, but expensive prices.