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.

In our last lesson, we talked about temporal adverbs for events that have occurred in the recent past or "just now." This week, let's take a look at one of those adverbs that might cause you problems. But first, a little background: the German adjective letzt is usually translated as the English adjective "last, " as in das letzte Mal ("the last time") or in letzter Minute ("at the last minute"). However, the adverb letztens, which might easily be mistaken for "lastly," in fact means "recently," — quite a different meaning indeed. Here are a some examples of letztens from Yabla:

BANNER PLACEHOLDER

Ich war letztens mal bei Rammstein.

I was recently at Rammstein.

Caption 32, rheinmain Szene - Unheilig - „Der Graf“

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Wir haben letztens auf einer Veranstaltung gespielt, wo jede Band einen Song covern musste.

We recently played at an event where every band had to cover a song.

Caption 15, Sons of Sounds - Interview

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You can see how some misunderstandings might arise if you misunderstand letztens to mean "last of all" or something similar. But what German words can you use if you actually want to say "lastly," "in the end," or "ultimately?" The easiest German word to remember for native English speakers is probably letztlich: 

Letztlich ist so ein Gepard also auch nur ein Mensch.

Lastly, such a cheetah is also just [like] a human.

Caption 14, Für Tierfreunde - Geparden

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Letztlich scheitert der Gastgeber schon im Viertelfinale.

In the end, the host team already lost in the quarter finals.

Caption 33, Frauenfußball - 11 Freundinnen

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Habe ich letztlich besser gemacht gesehen.

I have ultimately seen it done better.

Caption 99, Free Birds - Interview mit Nora Tschirner & Rick Kavanian

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The adverb schließlich can have a similar meaning: 

Schließlich kamen sie an ein großes Wasser.

Finally they came to a great [body of] water.

Caption 27, Piggeldy und Frederick - Der Himmel

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As can the adverb zuletzt:

Mein Wahlspruch heißt: „Die Dummheit stirbt zuletzt“.

My campaign slogan is: "Stupidity is last to die."

Caption 43, Tom Gerhardt - Die Superbullen

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BANNER PLACEHOLDER

Further Learning
It's important to remember that letztlich, which is structurally very close to "lastly," also means just that, whereas letztens means "recently." Go to Yabla German and find different examples of letztens, letztlich, schließlich, and zuletzt to learn the different ways in which these words are used by native German speakers in a real-world context.