There are several ways to express "anyway" in German, depending on the function that the word is supposed to have. There are four main words to know, but you'd be surprised at which words can take on a similar meaning. 

Let's start with examples in which "anyway" has a confirming function, which can be expressed with eh, sowieso, or ohnehin. In the following sentences, there is a match in what is going on, or something may already be the case.

BANNER PLACEHOLDER

Ist das aber kalt! und schwimmen kann ich sowieso nicht.

Is that ever cold! and I can't swim anyway.

Captions 35-36, Piggeldy und Frederick - Der Himmel

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Ich hab ja auch eh nichts mehr zu verlieren.

I have nothing left to lose anyway.

Caption 11, Das Lügenbüro - Die Bewerbung

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...aber da ich ohnehin lieber ein Marmeladenbrot essen möchte,

...but since I'd rather have a slice of bread with marmalade anyway,

werd' ich jetzt rübergehen zum Brot und mir eine Scheibe Brot schneiden. 

I am going go over to the bread and cut myself a slice of bread. 

Captions 5-6, Jenny beim Frühstück - Teil 2

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However, eh and sowieso can't always be used. For sentences in which "anyway" has a contradictory meaning (and could potentially be replaced with "despite that" or "nevertheless"), trotzdem is the word you're looking for. 

Die Hühner legten aber trotzdem weiter Eier

But the chickens kept laying eggs anyway,

und sogar mehr als sonst.

and even more than usual.

Captions 17-18, Cettina und Sabine - Ostern

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Hätte ich voll Angst vor, aber würde ich trotzdem machen.

I would be totally afraid of it, but I would do it anyway.

Caption 51, Free Birds - Interview mit Nora Tschirner & Rick Kavanian

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There is then also a conversational "anyway," which various words in German provide in particular contexts. As you will notice right away, these words are not always or even usually translated as "anyway," but the equivalent phrase uses it to express the intended meaning. 

Gut. Und wo befindet sich Bayern überhaupt?

Good. And where is Bavaria located anyway?

Caption 10, Bundesländer und ihre Rezepte - Bayern

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Wer braucht schon Hollywood?

Who needs Hollywood anyway?

Caption 1, Berlinale - Schauspieler Jürgen Vogel

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Wie alt ist er denn?

How old is he anyway?

Caption 8, Ein Herz für Tiere - Tierschutzhof und Border Collie

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Na, jedenfalls, arbeiten wir mit sechs Kameras.

Well, anyway, we'll be working with six cameras.

Caption 34, Otto Waalkes - Hier kommt Otto!

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Na ja, wie auch immer, also, wie Sie das mit der Kerze hingekriegt haben, das war... fantastisch.

Well, anyway, so, however you did that with the candle, that was... fantastic.

Caption 13, Weihnachtsmann gesucht - Bist du verliebt?

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Further Learning
You can find many examples of sowieso, eh, ohnehin, and trotzdem being used on Yabla German. When you see one, consider why the chosen word is being used. When you find yourself using the word "anyway," you can consider which German word would fit the particular meaning you are conveying.