Theories on how Trunks was conceived:
*Some time after Future Trunks came and went, warning the gang about the future androids and stuff.
One random day, a drunk Bulma walks into Vegeta.
Vegeta: Get out of my way.
Bulma looks up and realizes who she just bumped into.
Bulma: Heyyy VeGEEeetaaa. So Glad to see youuaa..
Vegeta: What the hell's wrong with you?
Bulma: Huhuhuhahahha~Nothing's wrong with me. In fact, I'm so happy about having sucha LOYAL boyfriend who CHEATS all the time. Which perfectly explains why I'm DROWNing my HAppiness with beeeerrrr-
Vegeta: Beer?
Bulma: YEssss. Sheeshhhh, have you neeevverr~ heard of ALCOHOL before? Huhuhuhahaha, (sacarstically) it's so powerful it can solve ALL your problems~! WANNA TRY SOME? I've got LOTS more to shareeee~Haaahahahhhaaaaaa
*Vegeta thinks of the awesome magical powers of senzu beans, then looks at the bottles in Bulma's hands.
Vegeta: Fine. *(Grabs the bottle and starts to drink)
5 minutes later, both of them are horribly drunk.
Bulma: And-And then, I ~(hic)~walked in on Yamcha with another girl.. Again! Ohhhh Whyyy is my life so miserable and unfairrr (hic)
Vegeta: Cheh, how trivial and petty your problems are.. Try having your whole planet DESTROYED, then being ENSLAVED by the murderer of your father for YEARS.. Then being overpowered by some low-classsss waaariorr like KAKAROOTT and now, some new kid from the FUTURrrree.. And I still can't acheive that SUPPER saiyan levell- Ughh
Bulma: Huhuhuhahahaha, that's funny ~(hic)~ You can't reach that level because you're not kind and PURE like Goku, sillyyy.. Huhuhuhahaha (hic)
Vegeta: Wha-What did youuu sayyy..? Ugh, why's the room spinningg.. You just saaid something, didn't you..? Why are there 2 of you in the room now..
Bulma: Huhuhahahaa, it's called being drunk, you dope... Ha-Have youu never been drunk beforeee?
Bulma moves closer and closer to Vegeta.
Bulma: Heeheehahaha, heyyy VeGEEeta, wanna try something? I think I've always wanted to try this out for some time now-(hic)
Vegeta: Ughhh.. Can't think properly now.. Yea, sure, fine, whatever..
Vegeta moves closer and closer to Bulma.
And thus, Trunks was conceived.
*Epilogue:
The next morning, Vegeta wakes up with a terrible headache and wanders around aimlessly until he accidentally bumps into Bulma.
Vegeta: What was that drink yesterday, woman... My head hurts...
Bulma: It's called having a hangover, you dope... Have you never had a hangover before?
Vegeta: Ugh, why does that sound strangely familiar..
Bulma: Do… Do you remember what happened last night?
Vegeta: Last... Last night..? I…
A sudden look of shock and realization crosses his face. Bulma looks hopefully at him.
Vegeta: YOU! I remember!
Bulma: Yes?
Vegeta: YOU SAID I COULDN'T ACHEIVE SUPER SAIYAN LEVEL BECAUSE I WASN'T OF PURE MIND
LIKE KAKAROT! I'M GONNA MAKE YOU EAT YOUR WORDS!
Bulma: ... Umm… Was there anything else you remembered?
Vegeta: WHO CARES? I'M GOING OFF TO OTHER PLANETS TO TRAIN, GET LOST.
Vegeta flies off, leaving Bulma behind.
Bulma: IDIOT VEGETA! I SWEAR I'M GONNA CURSE YOU EVERYDAY UNTIL YOU REMEMBER WHAT REALLY HAPPENED LAST NIGHT!
Vegeta looks behind momentarily and chuckles.
*Some time later, on some unfortunate planet experiencing an epic downfall of meteorites.
Vegeta: Waahahahahahaha! Take that! I can finally turn into a Super Saiyan!
Meanwhile, Bulma is still cursing Vegeta back on Earth. Vegeta sneezes again.
(Note: This is a reference to the belief that someone is talking behind your back whenever you sneeze)
Vegeta: Atchoo! ... ... ~Sniff~ ... ... DAMMIT BULMA! I REMEMBERED! STOP CURSING ME!