Water is a frequent concern in and around a bathtub, and having caulking or grout that is failing can be cause for catastrophic water damage. Ensure this doesn't happen by filling in any gaps that may be around your tub with a high-quality caulking. Larger gaps will require a little more prep work and care than smaller cracks, but with time, each one can be made watertight.
Fill your tub with water to ensure that each gap is at its widest point, then measure the width and depth of each void. If the gap is larger than 3/8-inch, consider using backer rod to give your caulking a firm foundation. Backer rod is a flexible piece of extruded foam that can be pressed into large gaps. You can do a neater job using it because less caulking is necessary. Backer rod helps prevent excess caulking from sagging out of the joint.
Silicone caulking can be more difficult to work with because you cannot clean it up with water (white spirit are needed) and it emits an odour while it dries -- but for large gaps, it is a must-have. Silicone caulks don't shrink as they dry and cure, and they stay flexible over time; acrylic latex-based caulking tends to dry out and crack. Silicone is also highly resistant to water, mould and mildew, which is important for a bathtub area where splashing is the norm.
Once you have applied the caulking, smooth out the bead of caulk. Many caulking manufacturers make tools for this purpose; if one is not readily available, a spoon or your finger will do the job in a pinch. Smoothing out the caulking has a twofold benefit for larger gaps: Not only will it improve the appearance, but it will also press the caulking back into the joint, helping to remove any air bubbles or voids that you cannot see.
Clean out the joint that you are caulking before you even cut the tip off the tube. Dig out any old caulking or grout using a utility knife or a removal tool. Then, use rubbing alcohol to remove the last traces of any old materials or oils from your fingers. After you have caulked the joint, clean up any excess with the appropriate solvent before it dries. If you used silicone, you'll need white spirit. Also, ensure you give the caulking plenty of time to cure before running water in the bathtub, and check to see if extended drying times are needed for larger beads of caulking.