Regeln:

Tanne - Tannen
Fisch - Fische
Fenster - Fenster
Gesetz - Gesetze
Handy - Handys

Das mit den Umlauten wird eher unter Ausnahmen laufen

(Glas - Glase gibt's übrigens auch, das sind die Glasarten)

Eindeutige Regeln scheint es nicht zu geben, aber gewisse Tendezen, wann welche der fünf Pluralendungen verwendet wird:
http://de.wikipedia.org/wiki/Plural#Pluralbil...

Edit: @ad.joe: Das sind doch einfach ein paar Beispiele, keine Regeln?

Sieh mal hier nach

http://www.canoo.net/services/OnlineGrammar/I...

Noch ein statistischer Aspekt zu den Pluralformen. Das ergibt dann 3 Regeln, die mit "Die meisten Maskulina/Feminina/Neutra bilden den Plural mit ... " beginnen ;-)

In some textbooks they don't talk about "rules" so much as "patterns." At least knowing that there's a limit might be helpful to some learners.

Here's one version:

http://books.google.de/books?id=brxvMZ8VgP8C...

(p.104 or search for "noun plurals")

Here's a table with more examples:
http://nthuleen.com/teach/grammar/pluralexpl.html

I can think of a few "rules" (of course there's exceptions) that I have learned over the years, though:
-Foreign nouns often take -s: Hotels, Taxis
-many masculine and neuter nouns ending in -er and -el don't change in plural: Lehrer, Kabel
-feminine nouns usually take an -n or -en: Türen, Gabeln (For Gabel, I always have to remember the 2nd rule, that it's just the m and n nouns that don't change.)

There are groups or patterns. For example 'Umlaut + e'. This is found with many masculine nouns and a few (very common) feminine nouns -- but NO neuter nouns. Neuter nouns with plurals in -e never have an Umlaut.

Conversely, all nouns with a plural in -er will have an Umlaut (if possible). Almost all of them are neuter, none are feminine, and otherwise you really just have Mann.

The problems mainly arise with knowing whether a masculine noun is just -e or Umlaut + e (or no ending, with or without Umlaut). And for neuter nouns, knowing whether it's -e or -er.

The list of non-feminine weak nouns (-en) ought to be learnt separately.

From the above, it should be clear that you really have to know the gender before you can form your own rules on plurals.