Rhonda Wellington Lloyd
Despite popular misconception Arnold does not consider Ruth is first crush no that tile goes to Rhonda.
When they are in second in grade he finds himself crushing on Rhonda. The feelings are brand new and he doesn't know what to do with them but it soon becomes a moot point because he sees the way Curly is acting towards Rhonda. He always felt that he was sensible and stepping out of the way for Curly feels that more prudent choice as he rather not get caught in the cross-hairs.
Ruth P. McDougal
He's being picked by a group of cruel kids, who call him orphan boy, a mama's boy without a mother and he can feel tears threatening to come out of his eyes when Rush appears and scares them off. The fact that she got them to back off and then comforted him means that he can't help but crush on her.
Nothing ever truly comes of it because Ruth isn't all that interested in dating someone younger than she is and Arnold has put her on a pedestal without realizing.
Iggy
Unlike Rhonda and Ruth, he truly isn't aware of his crush on Iggy. He just knows that he Iggy is cool and popular and is happy that Iggy likes spending time with him. When he finds out Iggy's secret he finds amusing and yet oddly endearing. However things spiral out of control with Sid and Stinky correctly guessing that he wears bunny pajamas and then the secret gets out.
When the dust settles he's angry at Iggy for not listening and he feels a deeper horrification at himself. His unaware crush dies a painful death and the friendship never recovers because he can't forgive Iggy or himself.
Miss Felter
The crush on Miss Felter is mainly because she's attractive and Gerald puts the idea in his head, nothing less, nothing more.
Lila Sawyer
No matter his insistent that he didn't write the note on the wall, no one is listening and so he goes on a date with Lila. He goes through the motion and when it's over, she moves on and he feels guilty for being cold to her. The crush on Lila is born with a realization that he did truly have fun, guilt that he was acting like a prick, and because Lila is genuinely a nice person.
The crush lasts throughout the rest of fourth grade and a little of fifth before it suddenly creeps on him that he only wants her as a friend.
Helga G. Pataki
It takes until sixth grade for to realize that he has had growing crush on Helga throughout the years. If Arnold is honest himself then Helga would be considered his first actual crush, the problem is that that Helga was too abrasive and mean for the young little boy to in first grade to realize the signs.
Most people think that Arnold having a crush on Helga would be a good thing because Helga loves him and that they would be a happy couple. The problem is that Arnold is well aware that everyone expects them to date and there's voice in his head asking if he truly wants to date Helga because he likes her or because everyone expects him too.
Every time someone makes a comment or a teacher pairs them to work on a group assignment together, the question enters his mind and he finds that he doesn't know the answer. In the end the crush on Helga dies because fundamentally Arnold is a good person and cares about Helga too much to cause her pain if it turns out that he ultimately dates her because it's expected of him.
Lorenzo
When their in eighth grade he finds things becoming awkward with Lorenzo, a sudden brush of the hand is enough for him to feel a blush a coming, he finds himself feeling too excited when Lorenzo wants to hang out, is becoming aware of how attractive he is, and is growing aware that people are beginning to react to it.
Eugene stares at him with something akin to stunned disbelief and naked hope, Ernie raises an eye brow and offers his hammer for protection if he needs it, Gerald look like he wants to ask him something or is waiting for him to say something, Lila and Phoebe keep looking towards Helga whenever he and Lorenzo are in close proximity, and Helga eyes unnerve him because he can't see behind the sheer storm of blankness of it all when their eyes do meet.
But Lorenzo smiles at him, makes his legs quiver, and his stomach a flutter and when Lorenzo kisses him one day, he eagerly kisses back and feels that everything is going to be okay.
Author's Note: I consider Arnold someone who fundamentally wants to be a good person and there's nothing crueler than playing with someone's feelings. Therefore if he's in doubt on why he wants to date someone, then he wouldn't date them in the first place.
The thing with Iggy is a combination of finding a crush being a well reasoned answer as to why Arnold went that far and finding the idea of Arnold not realizing that he was crushing on someone rather funny. That however did create a plot bunny of Arnold being Bi hence Lorenzo, who I picked because I wanted something completely different from the pairings I've seen on here.