Japanese is a language in the Altaic language family, which is very small and, surprising as it is to many, not related to Chinese in any other way except for writing. Oftentimes, a misconception is that Japanese is a very difficult language that lays on the politeness much more thickly than most Westerners are used to, but to sum up this language of the rising sun is hardly a full, accurate picture. Yes, there are Chinese characters in Japanese, and yes, Japanese grammar can be tricky, but I believe it is easier to learn than many Western languages.
Why learn Japanese? I began learning Japanese partly out of necessity (I needed two classes of a foreign language at my college) and partly for entertainment, because yes, I am a fan of anime. Part of my comic book collection includes a few books that were imported from Japan, written exclusively in Japanese. You do not need to be an anime fan to have a reason to learn Japanese, though. There are many other reasons to learn. America gets many of its cars and especially electronics, whether for good or ill, from Japanese companies, and these manufacturers often have plants and offices here in the states. Besides that, there are some very good programs, such as the government-sponsored JET, which take native English speakers and pay them to help out in English classrooms in Japan. While knowledge of the Japanese language is not necessary to work for JET or any of the public "eikaiwa" (English conversation schools), it would certainly be useful.
One of the easiest aspects of learning Japanese is actually the pronounciation. When reading Japanese that has been written in the Latin alphabet (called "romaji"), everything is pronounced exactly how it looks, and pronounciation is not changed by a word's "gender" (unlike many European languages, like Spanish or German, words have no "gender," at least not in that way) or position next to another word. The only rule to keep in mind, and where English speakers tend to screw up, is that each syllable gets equal time, and syllables have only one vowel. So, it's "tou-kyou" not "to-ki-yo" for Tokyo.
Writing is the tricky part of Japanese, and what everyone seems to get scared about. Why? There are four writing scripts, oh no! The first one is romaji, which is just Japanese written in the Latin alphabet. So, you already know romaji. Pat yourself on the back! Next there is hiragana. Hiragana each represent a sound in Japanese, each sound being a syllable, and they can be recognized by their swirly, curvy design. There are in total 46 of them, oh no! Many are not unique but are used in conjunction with another smaller hiragana, so "ki" and a little "yo" equal "kyo." Hash marks in the corner of a hiragana make a "sa" into "za," a "ha" into "ba," and so on. Hiragana is mostly used in Japanese writing for verb endings and grammatical markers called "particles," with the other characters being those Chinese characters which are called "kanji." However, many books geared towards the kids, such as most manga (comic books), us furigana, or tiny hiragana printed above the kanji to tell you how it's pronounced! Yayness, now you don't need to know all 2,000 reguarly used kanji in everyday Japanese. With romaji, hiragana, and kanji, there's three. The last one to know is katakana, which is absolutely necessary and will get you far in the language. Those are the angular-looking characters. Guess what they're used for? You've probably seen them on video game packaging. Katakana are used for transcribing foreign words into Japanese (and plants, for some reason my native Japanese speaking professor could not answer). Some foreign words that are written in katakana, words that are very important to learn, are "hanbaaga" (a hamburger), "furansu" (France), and "bideo geemu" (video game).
Grammar in Japanese doesn't have a lot of tricky rules, but they are very different than English. Without practice, it can be difficult for a native English speaker to get used to, because the word order seems backwards to us. We say, "I threw the ball." Japanese people say, in Japanese, "I (the) ball threw." Verbs end the sentence, period. The subject part of a sentence, such as "I" or "you" or "such and such person" is often left out completely if it is already understood who or what the sentence is about. It is perfectly acceptable to say in Japanese, "Onamae wa Bob desu," or "name is Bob," because if you're giving your name, obviously you're talking about yourself. Saying "I am" in that case is just too formal.
Formality is a big concern for Westerners who grew up with the stereotype that Japanese always say "oh honorable" or "honorable this and that" all of the time. That's a bit silly. Some words, like "namae" (meaning name, just like in the above paragraph), do get an "o" or "go" that gives honor or respect to the word. There are also some customs, mostly used by store clerks and the like (i.e., people trying to sell you something), but you just need to know that "keigo" (polite speech), as it's called, requires using polite verb-endings and calling people by their last name with the suffix "-san." Luckily, Japanese classes teach the polite verb endings first because they are actually easier! You'll eventually need to know plain verb endings in order to conjugate verbs, but starting out with keigo is easier and avoids coming off as rude if you talk to Japanese people. When you do learn plain Japanese verbs, your Japanese friends will let you know when it's okay to switch to regular talk by saying something like, "What's with the keigo, man?" Or they might say, "What's with the 'san' on my name? Aren't we buds?" Being a gaijin (foreigner), it's a good rule of thumb.
One more piece of advice about Japanese: when using English words that Japanese people have incorporated into their language, don't assume they are pronounced the same way or even mean the same thing. When in doubt, check a dictionary.
Think you want to learn Japanese? Though pricey, the Genki series is a great text used by colleges that you can buy used online. There's also a couple of great websites that allow you to drill vocabulary and kanji, like Renshuu.org or WordChamp.Com. WordChamp has sound clips that are great for hearing as you drill, but I love that Renshuu is geared towards just Japanese and has such an extensive library of drills, test guides, grammar, and more. Also consider buying a few comic books in Japanese. Sasuga Books at sasugabooks.com is a good importer that carries most everything, and it is a real brick-and-mortar store in Boston. Shipping takes awhile, but with most comics geared towards kids who don't know all their Chinese characters yet, they make good reading. Jim Breen's online dictionary is awesome and will translate any words (http://www.csse.monash.edu.au/~jwb/japanese.html). I also own one of those "250 Everyday Kanji" or whatever, which have little pictures showing how the kanji were developed out of pictographs, very useful for remembering. Watch Crunchy Roll videos at crunchyroll.com, to hear Japanese spoken. The best way is to actually go to Japan, but since we can't all do that, do give my suggested resources a try!