What nightscrawl said.
If you don't want to perform the Dark Ritual with Morrigan, you've got a few options:
1) If you want both your Warden and King Alistair to survive but just don't personally want be the one to make a baby with Morrigan, you can always have Alistair perform the ritual with her. That way, neither of you have to die and you don't have to be the one to sleep with Morrigan; your Warden can ride off into the sunset with Leliana, and Alistair can remain King.
2) If you want both your Warden and King Alistair to survive but just don't want to do the ritual period, then if you harden Alistair and have him agree to become King and enter an arranged marriage with Anora before the Landsmeet, then you can recruit Loghain to sacrifice to the Archdemon without getting Alistair so mad that he refuses to become king and goes off to become a wandering drunk. (If you recruit Loghain he always leaves your party in disgust, but if hardened and made to agreed to marry Anora before the Landsmeet he'll honor his agreement even though he's furious about the situation). That way, after you refuse Morrigan's ritual then you can just have Loghain sacrifice himself to the Archdemon, that way you'll survive the Blight and King Alistair will still lead Ferelden, even though he's still mad at you.
3) What nightscrawl said. You can die slaying the Archdemon by either hardening Alistair and convincing him you should be the one to do it, or leave him at the gate below. Or just let Alistair sacrifice himself.
Your Warden can still come back for the expansion and DLCs even if you died performing the ultimate sacrifice, but it's kind of silly since none of the characters acknowledge that you're supposed to be dead. If you don't import your character, then you have to use a new, generic Orlesian Warden with the "standard" worldstae, but your choices from the main game can't be imported. (Kind of ridiculous, in my opinion.)
King Alistair in future games: Since different worldstates have to account for so many player choices, they're not strictly that big a deal in the long run. If you make Alistair king, he only makes a quick cameo in Awakening, DA2, and DAI, and that's it. (Even if you don't personally like Anora, the country doesn't fall to chaos with her on the throne.)
Morrigan in future games: She still shows up in Witch Hunt and DAI, but her dialogue and character development changes based on whether you befriended her, romanced her, and/or gave her a kid. She's obviously much warmer if you befriended and/or romanced her. If you had a kid with her, obviously she's sweet because she had a child with the man she loves. If she got pregnant through other means (like Alistair performing the Dark Ritual for us Lady Wardens), she's still much warmer person because raising a child taught her so much.
We still don't know what Morrigan (and/or Flemeth) intends to do with the soul of the Old God, but so far nothing nefarious has happened. Since BioWare has to account for worldstates where Morrigan didn't do the ritual, I'm guessing it's not super plot-changing. But personally I LOVE Morrigan as a mother; she's grown so much as a person. To me, the kid with the Old God's soul is so interesting (you'll see when you get there), so I personally think the kid is worth his weight in gold. I have a hard time making a worldstate without him.
Finally, worldstates: You can directly upload DAO save files into DA2, but you can't upload any DAO or DA2 save files into DAI. For that, you have to use the Dragon Age Keep, where you personally hand-craft every DAO and DA2 worldstate to upload into DAI if you don't want to use DAI's default worldstate (female Dalish Warden who sacrificed herself to the Archdemon, for starters). It's not so bad since every quest comes with a "default" choice, so you just change it to suit your world worldstate as you go. The Keep also lets you make at least ten worldstates to upload into DAI, so you don't have to worry about having all your Wardens' saves on file in order to upload into DAI. No fuss, no muss.