newjacks

1. Thinking chains are disposable and should be replaced when they start getting noisy/grimey.
This one I commited probably the first 8 months of riding fixed before realizing how easy it is to clean/re-lube a chain. I was coming from a background in riding beater 10-speeds on the street, and like most people who strictly ride absolutely **** bikes and don't know the difference between anything else, I figured noise was something that could only be replaced, not repaired. Either way, cleaning chains is cake and there are many guides online that explain it better than I could.

1.5. Buying Z-Chains.
Sometimes I still do this because there's no other option (in my college town atleast). But really, Z-Chains are probably the most carried and ****tiest 1/8" chain around. They stretch in a few months usually, and after that happens you have to throw them out. Better chain for similar dough IMO is the SRAM PC-1.

2. Thinking tubes are disposable.
It may seem easier to just replace a tube when you're a beginner, but with the rising price of tires and tubes these days (which corellates directly with the rising price of oil and falling dollar), it's a lot better idea to learn to patch and do it often in the case of flats. I used to be suspicious of patches and thought they'd come off but this turned out to be grounded in myth. Have a friend or shop show you the proper way to patch a tube / figure out where the tube got pierced, or just read the instructions that come with a patch kit.

3. Paying for rear tires (while running brakeless).
I'm sure a lot of people still do this. But when even the best tires get only a few months of skidding/skipping before they're time for the trash, this is kind of a mentally handicapped way to waste money. Bike shops throw out perfectly good tires every day, and either just put them in the dumpster, the back of the shop or a free box. If you're not sure where a shop puts said perfectly fine tires (and you already support them with your cash), ask someone who works there. But you obviously have to be careful as some tires are thrown out for a legitimate reason (i.e. they're trashed). Inspect all dumpster tires thoroughly or have a friend show you what to look for if you can't figure it out. Things like busted sidewalls, random gouges, exposed casing and damaged beads are some obvious ones.

4. Thinking things like clipless shoes, helmets and spandex are lame.
I know plenty of people are still under this assumption, but the truth is if you mature out of the little bubble of cycling for fashion or fixed gear freestyling and become aware of the greater world of bikes, you'll agree that none of these things are lame.

Clipless, first of all, is one of the most purely performance minded upgrades you can do, and a well-fitted clipless setup will make you faster and give you more control. If you start getting fast you'll appreciate the feel of them, but if you stay stuck in the world of cruising along at 13mph (not necessarily a bad thing), you won't.

Helmets - the more years you put into riding bikes, the more conscious you become of the vulnerable position you're in on a bike and the dangers you face all around you. It's not the ones you see, it's the ones who don't see you that you have to worry about when on the road and not turning into an adult vegetable. Now I personally don't wear my helmet as much as I should but the more I think about it, the more it becomes apparent that I should be using it every day.

Spandex - another thing you'll figure out as you mature as a rider is that spandex isn't some funny thing you put on to try and look like the pros or get more 'aerodynamic', it's an absolute necessity if you start actually putting in serious miles (25+). Butt chaffing is a horrible thing. You'd be surprised how many people wear spandex shorts underneath their regular old jeans too.

5. Trying to do too much mechanical stuff when you have no idea what you're doing.
I've been guilty of this before (tried to teach myself to true a rim and failed) and I've seen a lot of people do some insanely dangerous/janky **** because they thought they knew what they were doing. If you want to work on your bike it's best to have someone else show you the ropes firsthand instead of poking around blindly. I know there's a small percentage of people that are naturally gifted as mechanics but for the rest of us this should be the rule.
5.5 Running the wrong chain tension and/or having a fault chainline
****ing up a chainline is not something you want to do. But chain tension is also important and I've even caught experienced mechanics messing this up and running chains at the tightest possible setting. Learn early on what's the proper tension, what's too loose and risks you throwing a chain, and what's so tight it kills your efficiency and wears the drivetrain way too fast.

BFSSFG BONUS #6. Thinking you're faster than a roadie because you passed them up during your commute.
Yes, I was obviously guilty of this one and even made a thread about it. I added this to the list after seeing someone else make the same thread today. While some of us are indeed very fast and some roadies are not and stay in cat 5's for life, generally the guys in spandex you see around town put in way more mileage and way more effort than some newjack on a Pista. Why aren't they going fast in the city in relation to you? Many reasons really - just finishing a 60 mile ride in the country, taking a recovery day, starting a warmup, etc. Roadies that race know that they need to be in top condition on race day and are aware of the benefits of not constantly going all out.