  We find 9 nuclear cluster candidates in a sample of 14 edge-on, late-type
galaxies observed with HST/ACS. These clusters have magnitudes (M_I ~ -11) and
sizes (r_eff ~ 3pc) similar to those found in previous studies of face-on,
late-type spirals and dE galaxies. However, three of the nuclear clusters are
significantly flattened and show evidence for multiple, coincident structural
components. The elongations of these three clusters are aligned to within 10
degrees of the galaxies' major axes. Structurally, the flattened clusters are
well fit by a combination of a spheroid and a disk or ring. The nuclear cluster
disks/rings have F606W-F814W (~V-I) colors 0.3-0.6 magnitudes bluer than the
spheroid components, suggesting that the stars in these components have ages <
1 Gyr. In NGC 4244, the nearest of the nuclear clusters, we further constrain
the stellar populations and provide a lower limit on the dynamical mass via
spectroscopy. We also present tentative evidence that another of the nuclear
clusters (in NGC 4206) may also host a supermassive black hole. Based on our
observational results we propose an in situ formation mechanism for nuclear
clusters in which stars form episodically in compact nuclear disks, and then
lose angular momentum or heat vertically to form an older spheroidal structure.
We estimate the period between star formation episodes to be 0.5 Gyr and
discuss possible mechanisms for tranforming the disk-like components into
spheroids. We also note the connection between our objects and massive globular
clusters (e.g. $\omega$ Cen), UCDs, and SMBHs. (Abridged)
