In German there’s an important distinction between subordinating conjunctions, which send the verb to the end in the following (subordinated) clause, and coordinating conjunctions, which link two main clauses and keep each clause’s conjugated verb in the second position. There are only five one-word coordinating conjunctions – three main ones that you already know if you’ve made it this far, and two that are a bit less common. We’ve underlined the conjugated verbs so you can see how they stay in the second position in both clauses:

  Coordinating Conjunctions
und (and)  
Du machst das noch mal und ich gehe ohne dich.
You do that again and I’m going without you.
oder (or)  
Du hörst auf damit oder ich gehe.
You stop it or I’ll leave.
aber (but)  
Ich wollte es abholen, aber der Laden hatte schon zu.
I wanted to pick it up, but the store was already closed.
(but, and yet)
[more lyrical and nuanced than aber, often expresses a mild paradox (it's like this, and yet it's also like that)]

Jahre vergehen, doch die Liebe bleibt.

Years go by, but love remains.
(because, for)
[a bit softer than "weil" (next table) and often used when the hearer is already aware of the following explanation.]

Bleibe bei uns, denn es will Abend werden.
Stay with us, for evening is nigh.

The list of subordinating conjunctions is a bit longer. Again, we’ve underlined the verbs -- notice how they move to the end in the subordinate clause:

  Subordinating Conjunctions
dass (that)  
Ich will, dass du deine Hausaufgaben machst.
I want you to do your homework.
(literally I want that you do your homework)

Er sagte, dass er kommen würde.
He said (that) he’s coming.

[notice that "dass" is often required in German
where "that" is optional in English.]
(if, when)
du möchtest, kannst du bei mir bleiben.
If you’d like, you can stay with me.

Jeden Tag, wenn ich von der Schule nach Hause kam, wartete mein Hund schon vor der Tür.
Every day, when I came home from school, my dog was already waiting at the door.
"When" is a more differentiated concept in German than in English. "Wenn" is used for the present, future, and repeated events in the past ("Remember when we used to stay out all night long?"). For a single event in the past ("When I got there, the house was empty") you should use "als" (below).
immer wenn

Immer wenn
es regnet, muss ich an dich denken.
Whenever it rains, I think of you.
weil (because)
Ich komme zu spät, weil ich eine Reifenpanne hatte.
I'm arriving late because I had a flat tire.
Many Germans also use weil in speech as a coordinating conjunction, without moving the verb to the end afterwards. Often they're not even aware of it, although they would instantly see the mistake if it was used this way in writing. One possibility is that they’re doing it for sentences where the listener already knows the "reason" (as with denn above). Another is that they’re accommodating a longer subordinate clause that would be harder to understand with the verb at the end.
(as soon as)
Wir reden darüber, sobald ich zurück bin.
We'll talk about it as soon as I'm back.
bevor (before)  
Ich hoffe, wir sehen uns noch mal, bevor ich das Land verlasse.
I hope we see each other again before I leave the country.
Sie kamen an, nachdem alles schon vorbei war.
They arrived after everything was already over.

Nachdem alles vorbei war, konnten wir darüber reden.
After it was all over, we were able to talk about it.
(as, when, while)
Ich bin gestolpert, als ich aus dem Bus stieg.
I stumbled as I was getting off the bus.

[Again, als is for a single past event; use wenn for a repeated event.]
da (because, since)  
Sie fuhren gerne Rad, da ihnen die Bewegung gut tat.
They enjoyed cycling because being active did them good.
seit, seitdem
(since [a point in time])
Er konnte an nichts anderes mehr denken, seit[dem] er sie zum ersten Mal gesehen hatte.
He couldn't think of anything else since he had seen her for the first time.
ob (whether)  
Ich weiss nicht, ob er alt genug ist.
I don’t know whether he’s old enough.

Often translates to "if" in casual English, e.g. we’ll say "I don’t know if he’s old enough" rather than "I don’t know whether"
obwohl (although)  
Ich habe zugesagt, obwohl ich Bedenken hatte.
I agreed, although I had my doubts.
(so long as)
du hier bist, kannst du dich nützlich machen.
As long as you're here, you can make yourself useful.
(while, during)
du auf mich wartest, kannst du die Zeitung lesen.
While you're waiting for me, you can read the paper.
bis (until)  
Ich bleibe hier, bis du zurückkommst.
I'll wait here till you come back.