Amount is reached, then increases continually (xxx in the message equals yyy, but the backup continues, and both figures continue to increase.

This is the most worrysome, and can indicate a problem, but not necessarily.  

1. •Usually, it's the result of a file being changed and made much larger after Time Machine makes the initial estimate, but before it was actually copied.  This is fairly rare, but is more likely if you have a large database file or are running a Virtual Machine and are backing-up those files (most folks exclude them from Time Machine, per Time Machine FAQ #10).
   

2. •A large download that's in progress when a backup starts, and finishes before it ends, can cause this, too, as the estimate may count only the first, small portion.
   

3. •A directory problem on the disk(s)/partition(s) being backed-up that causes the estimate to be too low.   If it happens repeatedly, try Verifying all disks being backed-up, per #6 in Using Disk Utility.

Amount is reached, then increases to a new figure  

1. •Sometimes, when backing-up multiple disks and/or partitions, especially on older versions of OSX, the initial estimate Time Machine makes is correct, but it shows only the estimate for the first drive being backed-up.  Once it starts backing-up the next one, the estimate for that disk is added.

Amount suddenly gets smaller  

This is actually Time Machine making a second "pass" at the backup:  after the copying is complete, it checks for more changes made during the backup.  If there are any, it will make a second pass to "catch up" with those changes, so your files aren't very far "out of sync."  This is almost always a very small and quick process, but after a long backup, such as the first, full one, it can be substantial.

But instead of increasing the amount from the first pass, it resets the counts and starts over.

The actual backup is smaller than the estimate  

This is common;  the actual amount is usually somewhat smaller.  Several possibilities:

1. •As noted above, the estimate is made using the number of 4 KB blocks occupied by the new or changed file or folder, but the actual amount copied is in bytes.  So a 100-byte file will be estimated at 4 KB.  Usually you won't notice this, but on an initial backup, or after an OSX update, there will be many thousands of mostly very small new or changed files in the System and Applications folders, so the cumulative difference may be substantial.
   

2. •Multiple changes to the same file can cause this, too.  If a file was changed several times since the prior backup, it may be counted more than once for the estimate, but of course only backed-up once. 
   

3. •If a file was created or changed, then deleted, since the last backup, the addition or change will be counted in the estimate, but nothing will be backed-up.  This seems to apply, for example, to the OSX Installer app when you do an OSX upgrade;  it's added to your system, but as soon as the install is complete, it's deleted.
   

4. •If a disk image is not mounted at the beginning of a backup, but has changed since the last time it was backed-up, Time Machine will intend to back it up and add the size to the estimate.  But if it's mounted before it gets backed-up, Time Machine will skip it until the next time it's not mounted, so the actual amount backed-up will be less than the estimate.
   

5. •A directory problem on the disk(s)/partition(s) being backed-up that causes the estimate to be too high.   If it happens repeatedly, try Verifying all disks being backed-up, per #6 in Using Disk Utility.