I'm trying to compile a list of movie pairs where the sequel is better made/superior to the first one.?

You know. Like for example Alien and Aliens, and Terminator and T2. Another, I guess, would be Mad Max and The Road Warrior, although #2 is better but not by much.

I'm not talking about bad first movies that have nowhere to go but up. I mean great movies that spawn something more than great.

Also, why do you think the series usually tanks with numbers 3...4...5...how many Alien movies where there again?

In the following some movies that I thought the sequel (whether 2nd or 3rd or whatever) is better than the original movie and for most of them the box office numbers support the claim:

1.
a. Terminator 2 (Judgment Day)
b. Terminator

2.
a. LOTR: The Two Towers (and) LOTR: the Return of the King
b. LOTR: Fellowship of the Ring

3.
a. Matrix
b. Matrix 2 (Reloaded)

4.
a. Meet the Fockers
b. Meet the Parents

5.
a. Shrek 2
b. Shrek

6.
a. Batman Begins
b. "Better than all the previous 4 parts"

7.
a. Pirates of the Caribbean: Dead Man's Chest
b. Pirates of the Caribbean: The Curse of the Black Pearl

8.
a. Toy Story 2
b. Toy Story

9.
a. X-Men 3: The Last Stand
b. X-Men

10.
a. The Mummy Returns
b. The Mummy

11.
a. Bourne Ultimatum (and) Bourne Supremacy
b. Bourne Identity

12.
a. Home Alone 2: Lost in New York
b. Home Alone

But the fact remains that the originals are more often better than the sequels.

Oh by the way (just for the fun of it) there were 4 Alien movies as well as Alien Vs. Predator (a.k.a. AVP) and there is an upcoming sequel to AVP (its called Aliens vs. Predator: Requiem), So by the end of the year there will be a total of 6!

the harry potter movies

i really liked shrek 2 a bit more that the first

Well, you took my first thoughts--Alien/s, T1&2.

Empire Strikes Back
Star Trek II (Khan)

To me i think " The nightmares on Elm street" horrors a the best. And there is three for Aliens movies and if you count 'Aliens vers pred' there is another two, one already out and the other is coming soon.

The Empire Strikes Back
The Godfather Part II
Desperado
Aliens, T2 and The Road Warrior I agree with as well

There are...6 Alien movies (Alien, Aliens, Alien 3, Alien Resurrection, Alien vs. Predator and soon to be Alien vs. Predator 2)

Sequels get worse and worse because the writers get lazier and lazier and instead of thinking of new stuff they just reinvent the wheel