i believe the OP is looking for an Android app that reads *vector* topo maps for the US. unfortunately, on Android there is currently no great option for this. nearly every "topo" map/gps app on Android uses *raster* tile-based maps. most even use the same free map sources, with a few offering paid-for maps or proprietary variations of public map sources. highly detailed raster maps are always going to take up a ton of space and therefore time to download.
Delorme, Garmin and Magellan are about the only companies with good vector-based topo data. i assume they all source it from similar bigger providers but then put their spin on it. the problem is none of them have created Android apps to work with their proprietary maps yet. the exception is Delorme, but my understanding is you have to have to own their InReach device in order to use their Earthmate app. i don't have the device so i can't say if the maps are the same as their PC US Topo series (which are great).
OruxMaps (free or $2.62 donation version) seems to be the only app working towards a vector-based solution. it's primarily a tile-based app too, but they have been developing support for the Garmin ".img" format. it still doesn't render the maps anywhere close to how Basecamp or a Garmin device would though, in fact i find them unusable personally. you also have to jump through a couple hoops to get a file from somewhere like GPSFileDepot.com into Orux as a single map.
there is a completely different vector solution gaining steam, geo-referenced PDF files. the app PDF Maps from Avenza shows promise, but it's very young and doesn't have a ton of good maps for purchase yet. it's one of those technologies that could become the gold standard or might completely disappear into obscurity. some volunteers in Colorado are working to keep up-to-date versions of all the MVUMs available in this format:
http://www.staythetrail.org/mvum/
now for "road" maps, there are several popular vector-based apps including CoPilot, Sygic, and TomTom. i use CoPilot for my on-road mapping and navigation and it's pretty good. the entire US including route and POI data is under 2GB and is a one-time download (plus free updates). it actually has most forest roads, but i still like to have topo maps in a separate app in order to see old tracks, mines, cabins, and the terrain features.
side note - if you have an iOS device, check these out:
http://www.benchmarkmaps.com/products-page/mobile-apps/ - Benchmark's printed Road & Recreation atlas are my favorite maps hands down. i'm eager for these to come to Android and hopefully have more states available soon too.
sorry for the long post, hopefully it helps someone!