Ok, so I got a brand now wheel for my road bike recently and bottom bracket. Everything is the proper size and such. Before though, when I pedaled backwards it had no problem and went smoothly. Now, the chain just chugs along when pedaling backwards as if it feels loose or something. But no problems when pedaling forward. Anyone know what I should do? Thanks!

Need different words than "chain just chugs along." Pictures might help, video even more maybe.

I'm not sure what you are describing? If the chain is hanging up when peddling backwards, likely the rear derailleur needs a slight adjustment. Or the B-screw on the derailleur needs adjustment.
Since you had the bottom bracket changed, I assume the correct width of spindle was used and you have a good chainline.

If the derailleur is out of adjustment, or you are cross chained, the chain will not line up with the cog when pedalling backwards.
More detail would be helpful.

Did you used to have a fixed gear wheel and now you have a single speed, so before when you pedaled backwards the wheel would move that direction and now it just coasts?

...check the freewheel or freehub in your brand new wheel for stiffness/tightness in the freewheeling direction.

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...I can already tell this will be entertaining as a thread. :

I'd use classic diagnosis methods. Separate from each other the various aspects of the system. Remove the chain from the cranks then spin the cranks. Do they rotate freely? Remove the rear wheel from the frame. Does it's cogs (cassette or freewheel) rotate freely? Spin each der pulley. How easily do they rotate? What about the chain? As you run it through your fingers do all the links freely hinge both ways?

Then there's the aspect of which cog/ring combos have the problem. All or just the ones that are cross chaining ones? Are you sure the rear der is staying centered under the cog which has the chain of it? Are there any bent or twisted teeth or links?

All this should take a trained wrench about 2 or 3 minutes to look at. We do this all the time when we take a bike in for service, on the spot with the customer often watching. No rocket science, no curtains or mirrors. Just common sense and basic understandings being applied. Andy.

First issue to resolve: why do you need to be able to pedal backwards?

Among other things I have always considered the ability to turn the crank backward was some what of a check that everything is ok with the chain and RD. If it wont smoothly turn backward, something is not right. It can be the RD, the adjustment of the RD, or maybe the RD drop out is bent. I mainly turn the chain backward to wipe it down before or after a ride.

I do that to check my saddle height, heels on pedals, set seat so I can pedal backwards without hips rocking. I may refine that setting but my current seat post moves down, and my inseam moves up (getting 60 lbs thinner will do that), and I have tried a few different saddles so it is a quick and dirty way to check saddle height.

Bill

Exactly, a swift backward kick of the pedals before every ride is a good idea.

If you moved your cassette to another wheel, you may need to adjust RD tension and sometimes the stops.
Put the chain on the 2nd or 3rd cog and adjust the tension until it almost touches the next larger cog.

If the Guide pulley is not directly under the cog , then back pedaling can pull the chain off the cog.

Was the chain removed and re-installed. I've seen chains improperly threaded thru the rear derailer (over the tab) that seemed to work sort of OK in the forward direction but fouled up and jammed the der when pedaled backwards.

+1, the freehub or freewheel ratchet may be a bit sticky or gummy adding some extra drag. This isn't rare with new hubs or wheels, since the lube can dry slightly on the shelf. The added friction causes the freewheel to drag, transferring slack from the lower to the upper loop when you backpedal.

The cure is usually a matter of adding 2 drops of oil to the freehub to soften dried grease. You can also ride a while and the problem may resolve over a few days as the internals loosen up with use.

There are also other causes of freehub drag, so if oil doesn't help, have someone take a look at at.

I think this was the issue I was having. But I will see to it if I can make a video of the issue as well so you guys can see the problem I was having. But let me rephrase that when it comes to pedaling backwards, I can and cant a times. Basically its always been when I use to pedal backwards the wheel never moved backwards. And now when I do pedal backwards the wheels moves backwards. Vice versa on that end which I know isn't suppose to do and rather instead make that clicking sound.

If it's this, you'll also see noticeable slackening or sagging of the upper loop when coasting. Lift the bike and spin the rear wheel forward and check.

Ok, so this is what it looks like when I pedal it backwards, and it never used to do this: https://www.dropbox.com/s/uc9w19zpwt...N1399.MOV?dl=0

This points to a sticky freehub, but doesn't confirm because the binding might be within the RD, or because of poor trim.

The coincidence of the timing points to the wheel since that's what changed. However, if you do the coasting test and the upper loop sags measurably that will provide confirmation.

As you have the bike upside down all you have to do is substitute "lower" for upper in FB's note above. Your freehub is probably sticking for some reason. Test by unshipping the chain from the cogs in the rear and try to stop the freewheel. If you feel a lot of resistance that is the problem, if not, check the derailleur pulleys. Google clean (or lubricate) freehub.

Did you adjust the RD to the new wheel? Unless you have the same model of hub as before the location of the freewheel/cassette is usually a little off. Even from the same manufacturer this could be the case.

Check that out along with the ability of the freehub/freewheel to smoothly turn backwards.

Yes, whenever I say upper or lower chain loop, I'm referring to them as they are with the bike upright. So the upper loop is still the upper loop even when it's on the bottom.

BTW- all this could have been avoided with a simple test that should be done before installing a new wheel.

Hold the wheel by the axle and spin it forward. Put your thumb against the cassette and you should only feel a trace of drag when it freewheels.

Some people simply spin the cassette and see how long it spins, but weight or inertia can affect that.

In any case, however you do it, check new wheels to confirm that the freewheel is truly free before installing.

Ok, this is what I tried. For he bracket that was in the back, I held it in place with my hand. I spun the wheel, and that bracket does indeed feel like its tight. I think thats why I am having the problem right now with whats going on. So its just the bracket then that needs to be loosened up I think?

If "bracket" means sprocket cassette or the ratchet mechanism inside, then "loosening" may or may not be appropriate. It's probably sticky with dried grease, not actually tight. So the answer isn't to loosen it but to add some oil to make it run more freely or "looser".

How to add the oil varies slightly with the type of hub. If you bought the wheel locally, let the seller fix this for you, or seek out a bike co-op, or a knowledgeable friend for help. (if you put where you live into your profile, someone might point you to a local resource).

Ok, thanks! Turns out this was in fact the problems I had. Runs smoothly now. But I think in the process I kinda messed up my breaks as well for whatever reason too. They dont seem aligned straight. Is there a way to adjust that? And no, I dont have any broken or loose spokes on that end.