How many bytes does one Unicode character take?

I know this question is old and already has an accepted answer, but I want to offer a few examples (hoping it'll be useful to someone).

As far as I know old ASCII characters took one byte per character.

Right. Actually, since ASCII is a 7-bit encoding, it supports 128 codes (95 of which are printable), so it only uses half a byte (if that makes any sense).

How many bytes does a Unicode character require?

Unicode just maps characters to codepoints. It doesn't define how to encode them. A text file does not contain Unicode characters, but bytes/octets that may represent Unicode characters.

I assume that one Unicode character can contain every possible character from any language - am I correct?

No. But almost. So basically yes. But still no.

So how many bytes does it need per character?

Same as your 2nd question.

And what do UTF-7, UTF-6, UTF-16 etc mean? Are they some kind Unicode versions?

No, those are encodings. They define how bytes/octets should represent Unicode characters.

A couple of examples. If some of those cannot be displayed in your browser (probably because the font doesn't support them), go to http://codepoints.net/U+1F6AA (replace 1F6AA with the codepoint in hex) to see an image.

1. • U+0061 LATIN SMALL LETTER A: a
     • Nº: 97
     • UTF-8: 61
     • UTF-16: 00 61
2. • U+00A9 COPYRIGHT SIGN: ©
     • Nº: 169
     • UTF-8: C2 A9
     • UTF-16: 00 A9
   • U+00AE REGISTERED SIGN: ®
     • Nº: 174
     • UTF-8: C2 AE
     • UTF-16: 00 AE
3. • U+1337 ETHIOPIC SYLLABLE PHWA: ጷ
     • Nº: 4919
     • UTF-8: E1 8C B7
     • UTF-16: 13 37
   • U+2014 EM DASH: —
     • Nº: 8212
     • UTF-8: E2 80 94
     • UTF-16: 20 14
   • U+2030 PER MILLE SIGN: ‰
     • Nº: 8240
     • UTF-8: E2 80 B0
     • UTF-16: 20 30
   • U+20AC EURO SIGN: €
     • Nº: 8364
     • UTF-8: E2 82 AC
     • UTF-16: 20 AC
   • U+2122 TRADE MARK SIGN: ™
     • Nº: 8482
     • UTF-8: E2 84 A2
     • UTF-16: 21 22
   • U+2603 SNOWMAN: ☃
     • Nº: 9731
     • UTF-8: E2 98 83
     • UTF-16: 26 03
   • U+260E BLACK TELEPHONE: ☎
     • Nº: 9742
     • UTF-8: E2 98 8E
     • UTF-16: 26 0E
   • U+2614 UMBRELLA WITH RAIN DROPS: ☔
     • Nº: 9748
     • UTF-8: E2 98 94
     • UTF-16: 26 14
   • U+263A WHITE SMILING FACE: ☺
     • Nº: 9786
     • UTF-8: E2 98 BA
     • UTF-16: 26 3A
   • U+2691 BLACK FLAG: ⚑
     • Nº: 9873
     • UTF-8: E2 9A 91
     • UTF-16: 26 91
   • U+269B ATOM SYMBOL: ⚛
     • Nº: 9883
     • UTF-8: E2 9A 9B
     • UTF-16: 26 9B
   • U+2708 AIRPLANE: ✈
     • Nº: 9992
     • UTF-8: E2 9C 88
     • UTF-16: 27 08
   • U+271E SHADOWED WHITE LATIN CROSS: ✞
     • Nº: 10014
     • UTF-8: E2 9C 9E
     • UTF-16: 27 1E
   • U+3020 POSTAL MARK FACE: 〠
     • Nº: 12320
     • UTF-8: E3 80 A0
     • UTF-16: 30 20
   • U+8089 CJK UNIFIED IDEOGRAPH-8089: 肉
     • Nº: 32905
     • UTF-8: E8 82 89
     • UTF-16: 80 89
4. • U+1F4A9 PILE OF POO: 💩
     • Nº: 128169
     • UTF-8: F0 9F 92 A9
     • UTF-16: D8 3D DC A9
   • U+1F680 ROCKET: 🚀
     • Nº: 128640
     • UTF-8: F0 9F 9A 80
     • UTF-16: D8 3D DE 80

Okay I'm getting carried away...

Fun facts:

• If you're looking for a specific character, you can copy&paste it on http://codepoints.net/.
• I wasted a lot of time on this useless list (but it's sorted!).
• MySQL has a charset called "utf8" which actually does not support characters longer than 3 bytes. So you can't insert a pile of poo, the field will be silently truncated. Use "utf8mb4" instead.
• There's a snowman test page (unicodesnowmanforyou.com).

Strangely enough, nobody pointed out how to calculate how many bytes is taking one Unicode char. Here is the rule for UTF-8 encoded strings:

Binary    Hex          Comments
0xxxxxxx  0x00..0x7F   Only byte of a 1-byte character encoding
10xxxxxx  0x80..0xBF   Continuation byte: one of 1-3 bytes following the first
110xxxxx  0xC0..0xDF   First byte of a 2-byte character encoding
1110xxxx  0xE0..0xEF   First byte of a 3-byte character encoding
11110xxx  0xF0..0xF7   First byte of a 4-byte character encoding

So the quick answer is: it takes 1 to 4 bytes, depending on the first one which will indicate how many bytes it'll take up.

You won't see a simple answer because there isn't one.

First, Unicode doesn't contain "every character from every language", although it sure does try.

Unicode itself is a mapping, it defines codepoints and a codepoint is a number, associated with usually a character. I say usually because there are concepts like combining characters. You may be familiar with things like accents, or umlauts. Those can be used with another character, such as an a or a u to create a new logical character. A character therefore can consist of 1 or more codepoints.

To be useful in computing systems we need to choose a representation for this information. Those are the various unicode encodings, such as utf-8, utf-16le, utf-32 etc. They are distinguished largely by the size of of their codeunits. UTF-32 is the simplest encoding, it has a codeunit that is 32bits, which means an individual codepoint fits comfortably into a codeunit. The other encodings will have situations where a codepoint will need multiple codeunits, or that particular codepoint can't be represented in the encoding at all (this is a problem for instance with UCS-2).

Because of the flexibility of combining characters, even within a given encoding the number of bytes per character can vary depending on the character and the normalization form. This is a protocol for dealing with characters which have more than one representation (you can say "an 'a' with an accent" which is 2 codepoints, one of which is a combining char or "accented 'a'" which is one codepoint).