What parts of a bike could potentially be harmed by degreaser? I'v been using citrus degreaser to clean my bikes for years. I usually get a gallon jug of it from the auto parts store, and it lasts a long time. I use it for cleaning the drivtrain, either using a chain cleaner or by soaking the chain overnight. I've used it with a rag to clean the rims. I'll sometimes even use it to scrub a nasty bit of dirt or grease off the frame. However, some of the discussion in this very good question has got me wondering: 

Are there parts of your bike that can be damaged by degreaser? Obviously, keep it away from the bar tape or a leather saddle, but what mechanical parts could be harmed by citrus degreaser? Also, are there types of degreaser out there that are gentler and could be more appropriate?
Degreaser acts like a solvent (although I'm unsure if it is technically a solvent, or more of an emulsifier).  With all solvents you'll have to be careful with what they contact--however degreaser is relatively safe compared to stronger solvents.

Each type of solvent has its own list of things it will dissolve--and even brand-to-brand can make a difference, so spot-testing is always recommended.

In general though, the risky things are:


Rubbers
Adhesives
Organics (leather, etc)
Porous materials
Paints
(obviously) Grease/lubricants


Your main concerns should be your tires, your paint, and (as you mentioned) components like grip-tape and seats.  Getting degreaser on these has the potential to stain--so extra precautions may be in order.  Typically your best option is to try and prevent it from contacting them, and cleaning it off quickly with mild soap &amp; water if you do make a mess (although soap and water itself will stain things such as leather if you're not careful).

A secondary concern is that you fully remove the solvent after it's done.  Leaving excess solvent/degreaser behind is a very bad idea--see Rubbing Alcohol below for tips.

As for other solvents/degreasers:


Rubbing Alcohol is fairly safe.  It has the risk of drying-out leather and rubber, but is very useful for cleaning parts--and especially useful for rinsing degreaser off of things such as chains (it also evaporates and leaves them dry--ideal for re-lubricating).
Naptha (a.k.a. liquid lighter fluid, not butane) can be very effective as well and is generally safe
Acetone is a stronger solvent, and likely to be less safe.  It should be used with extreme care, but is a very powerful solvent and can get the job done well and quickly.