I'm very interested in use cases with Arc Hydro and your experiences with it. Do you think it has an added value compared to standard Spatial Analyst analyses?
ArcHydro is fully dependent on ArcGIS, so no stand-alone use. And it's not comparable to Spatial Analyst in any way, as the tools in the latter are quite basic and don't help for hydrology-related studies (while they are okay for basic land system mapping).
As wrote Daniel, you can use HEC-HMS, but many models exist, more or less using ArcHydro or Spatial Analyst to generate inputs or processes. A very popular yet complicated model is SWAT (Soil Water Assessment Tool) that has an ArcGIS extension, but also WEPP, and the list is quite long, for extensions and for stand alone applications as well.
It finally depend if you're interested in process-based (hydrological model) modeling or empirical modeling (ArcHydro).
I have recently used Arc Hydro in a a study of urban drainage. From my experience, it works better than Spatial Analyst (Hydrology) when delineating watersheds. It seems that the latter can lead to errors when working with small areas.
In my case, I used it along with HEC-HMS (via HEC-GeoHMS).
ArcHydro is fully dependent on ArcGIS, so no stand-alone use. And it's not comparable to Spatial Analyst in any way, as the tools in the latter are quite basic and don't help for hydrology-related studies (while they are okay for basic land system mapping).
As wrote Daniel, you can use HEC-HMS, but many models exist, more or less using ArcHydro or Spatial Analyst to generate inputs or processes. A very popular yet complicated model is SWAT (Soil Water Assessment Tool) that has an ArcGIS extension, but also WEPP, and the list is quite long, for extensions and for stand alone applications as well.
It finally depend if you're interested in process-based (hydrological model) modeling or empirical modeling (ArcHydro).
Another piece of software to check out, in conjunction with the above answers, is: Indicators of Hydrologic Alteration (IHA) developed by the Nature Conservancy. This software is quite useful if you have multiple measurements in ungaged streams.
ArcHydro has a substantial set of tools for Hydrologic analysis as stated in other answers. It is similar to HEC-GeoHMS built on ArcGIS, which is a companion piece to HEC-RAS and HEC-GeoRAS. The only problem is those are typically lag time in development, so they are usually behind the latest release.
Both these tools are more tailored to Hydrologic and Hydraulic analysis, so will have more tools for that purpose the extensions. But, ArcHydro requires Spatial Analyst and 3D Analyst to generate the models/basins/watersheds etc. So in theory you could do the basic analyses on your own with the Raster Calculator.
ArcHydro uses Spatial Analyst to perform hydrological analyses such as Flowpath analysis, sink analysis, catchment delineation. I prefer to user Spatial Analyst directly. This way, I know precisely what I do. I combine the tools of Spatial Analyst and tools of the basic toolboxes. This way, it is possible to e.g. get Flowpaths classified by catchment area and sinks with properties like Area, Volume. In order to automate this, I usually use the ArcGIS Model Builder. But it is also possible to use python scripts.
However, a topological analysis you can perform with ArcHydro or directly with Spatial Analyst does not replace a numerical runoff model. It can be used to make a first assessment (e.g. of the flood risk) in order to determine the focus areas, where numerical models shall be applied.