Here are some ways to get things early.
Get the spazer early: You don't need high jump boots to get spazer if you know wall jump. Shoot at the hole in the upper left corner then wall jump up.
Super Bombs Early: You appear to need high jump boots and ice beam to get super bombs. Well you don't, you just have to be a good wall jumper. Kill the flying dudes with super missiles. Then wall jump up and stand on the little ledge to the right and shoot the blocks and just keep wall jumping up.
X-Ray scope Early (courtesy of Jack): You can get the X-Ray scope before getting the grappling hook. You have to have about 4 energy tanks, full health and the ice beam. The X-Ray scope is located in the bottom right part of brinstar and you have to go through a room that requires grappling to get to it, but here's how to do it without grappling beam. Do not kill any enemies in this area! After entering the room and reaching the edge of the top most floor, (where you're supposed to start grappling) fall down. Go to the very bottom and get as far to the right as you can, but make sure you're on flat ground. Start speed running to the left and jump, you'll almost make it to the ledge above. You can wall jump off of the thin ledge and get up there. Now here's the tricky part. Use your enemies as stepping stones, freeze them as they come by. After the second stationary enemy on the ground just run across the spikes until you reach the part where it starts to drop down. Fall down a little ways and there's one little platform you can stand on and not be hurt. Wait for a flying enemy to come by and freeze him. Jump on him and jump up to the platform with the door. You got the x-ray scope! Now to get back just run across the spikes. That's why it requires full health and a few tanks. You have to be pretty skilled to pull this off and I'm not sure if it's worth it.
It's not much and you have to be a good wall jumper but it could help some people.