1. Instant on. Turn on the switch ad the computer's booted. On some machines, you might have to wait for your DOS to load, but it was typically quick. No more waiting minutes (or sometimes hours in the case of Windows XP) to boot up.
2. As noted upthread, BASIC. Yeah, it was a crappy programming language. The microcomputer versions were pretty bad--line numbers, single letter variables, no structured programming constructs, lack of hexadecimal notation for POKEs, and slow speed. Debugging was nearly impossible as the language was prone to spaghetti code and it was hardly self documenting (who is going to waste precious memory on a REM statement?). Regardless, it was very straightforward to use and allowed novices to create something that worked. It forced people to learn how to code, as even the most basic of commands, like "LOAD "*",8,1 was a BASIC statement. If you wanted to do anything with the machine, you had to do something in BASIC. It was good for people to learn.
3. Games. The games were fun and didn't require investing a part of your soul and all of your spare time to play them. I still play some of them in emulation when I have some time to kill. they were unique, and there is nothing like them today.
4. Modems. Yeah, they were slow, but you had to love that handshake/connect sound!! It's amazing how much juice they managed to get out of them near the end. There is something very primal about connecting a computer via phone line. I miss it. I read recently that modems don't really work on VOIP lines, which is what most remaining land lines consist of. That's a big bummer...
5. The Atari Joystick Standard. I have a very hard time playing with a modern game controller with it's millions of buttons. Give me a one (I'll be generous, two) button joystick any day over these modern monstrosities.
6. Babbages. Yes, that came later, but a store devoted to computer gaming? Heaven! I had a friend who was a manager there. They were allowed to take home and "test drive" the software. I was so mad when he quit that job!!!
7. The simplicity and closeness to hardware. You can't manipulate hardware nowadays like you used to. Everything was easy to get to via software. The software itself was simple and straightforward. You don't get that today.
The things I don't miss:
1. Tape loading... who would be crazy to name that as a good thing? That was awful. There's a reason why everyone switched to floppies if they could.
2. Lack of access to information about your computer. The books and magazines were great, but getting the right book or back issues of the right magazine were often difficult to find... There was no access to code libraries or helpful info if you ran into a problem programming or using your machine.
3. Getting software. It could be tough finding retail outlets that sold your stuff, and very few things came at a discount. That was another good reason to learn how to program.
4. Single tasking. We are spoiled nowadays with our ability to run multiple programs at the same time. Back then, on some computers, just loading up a DOS file directory would cause you to lose all your work. Thanks to multitasking, we can emulate our beloved old computers at the same time we can do something else.. so overall, we certainly are better off today than before... but I still miss the old times.