Can I hand wash my clothes in the bathtub?

Besides it being a complete pain in the ass, no reason not to. The detergent won't harm your tub (might clean it a bit), and won't negatively affect the plumbing, either. Don't use too much detergent or you'll never be able to rinse it out like a machine can. I do predict, though, after one load you'll be willing to walk down the stairs and pay the $1.50 or so... :)

I often do a handwash in the sink if I only have a couple of small things. The soap is fine for your plumbing. The only issue is the sheer amount of work it'll be. Like jacquilynne said, you have to agitate, which means thoroughly kneading every single item of clothing you're washing, twice (once in soap and at least once in the rinse).

You can (one of my coworkers does it) but as pointed out above the effort to do it will me more than just walking downstairs.

If you are as lazy as you claim, you won't do more than one wash in a bath tub.

The detergent will not harm your tub, but it could harm your hands. I was in a situation where I had to hand wash all of my clothes. I used machine detergent and broke out into horrible contact dermatitis, which was insanely itchy. What you want to do is find a laundry bar that is meant for handwashing (or just use regular hand soap or shampoo, which is what I do for my few non-delicates that I continue to hand wash). Also, get yourself a little brush like a nail brush or a potato scrubber. If you are really serious, pick up a washing board at a junk store (note that you put the cloth against the board and scrub with the brush--not your hands! Hands will hurt!! I learned this the hard way when I was 12 or so.) Apply the soap to any soiled areas and the areas that most need cleaning (collar and armpits of shirt etc) and scrub those areas with the brush. Then leave the clothes to soak for a little while in the soapy water. If you're doing whites or have a lot of stains, you can use an oxygen bleach, which will also be fairly easy on your hands (although put it in during the soak period, not before). It shouldn't be too hard to rinse, since you weren't overusing a liquid soap. To help with the ringing process, you can use towels: once you've gotten most of the water out, lay your clothes out on a towel, wrap it up and gently press with hands or feet. Obviously, you won't want to do that with every piece, but if you have one or two that are particularly hard to wring, it's a helpful trick. Also good for things that don't hold their shape very well.

I did it for a year when I had no choice, and got used to it. But the minute I had the opportunity to carry all of my laundry right across town and hand it to a woman who would do it for me for not much money, I did - it's hard on the back to get down that low and do the necessary pummeling: harder than walking across town with a bag full of clothes. I don't know about the effect on the tub, as it was pretty rank to start with (student hall in post-Soviet Estonia, c. 1996, not known for shiny enamel bathware).

I'd just like to echo what carmen said: Yes, it's possible (I regularly do it when I have just a few items of clothing I want cleaned), but if you use machine wash soap it'll be hell on your hands. Put some effort into finding a hand wash soap that's effective and doesn't strip the top five layers of skin off your hands.

That's how my roommate and I washed clothes for four months when we took a semester abroad in Spain. We'd soak and agitate in the bathtub, do a couple of rinses, wring out the clothes (heavy and you have to wring them out really well, especially jeans!). We had a porch on our apartment and strung lines out to dry the clothes. It worked fine, but it is a pain to do - the bending/crouching/agitating/splashing and dripping water all over the bathroom while wringing out clothes and carrying them out to the line - and the clothes tend to dry stiff. The detergent shouldn't harm the tub or plumbing. I don't think you can be both lazy AND cheap here!

I did a full load in the tub a time or two during hard time. Honestly, it was exhausting, and it's SO hard to get them rung out. That spinning thing washing machines do is hard to recreate manually... not that you want to spin them, but you need to get water out, and it's really not any fun. The clothes are too wet to even hang. It made the shower curtain bar collapse.