Hiya,
In work environments we offer a Cloud Managed WiFi Solution that entails a mesh network of as many of our enterprise ready WiFi access points as are required to get the coverage you require. These come in different sizes depending on the number of expected wifi connections. These require a power socket and a network connection but are fully configured and managed via ourselves remotely.
For home environments the best solution depends entirely on the house as to what options you have. In order to get the strongest signal you should be looking at a Wireless N router which broadcasts its network across multiple wifi channels in order to get a better consistent range. One way to get a better quality signal is to disable your encryption on your wifi network as this consumes a lot of bandwidth and has a large overhead. So by turning WPA or WEP off you can gain quite a lot of range. The downside to this is that your network data is unencrypted. So you would then need to ensure you use alternative security measures to avoid others jumping on your wifi network and stealing your bandwidth such as MAC Address Filtering and hiding your SSID broadcasts which most routers support.
Other devices out there that help are wifi signal boosters. These do what they suggest but rely on having at least a half strength signal to the original wifi point. Otherwise what you get is laptops connecting at full signal to the wifi signal booster but then a bottleneck in traffic as it cant forward the data to the original access point. I have seen some houses with 3 or 4 of these chained in a row to give a house full coverage.
If you require wifi in two rooms at either ends of the house then you may want to look at creating a network using your houses electrical cabling infrastructure. Normally you need to plug a device into a 3 pin plug socket (not an extension). A network cable comes out of this into your broadband/wifi router.
Then at the other end of the house you plug another device into the 3 pin plug socket. Out of this you plug the network cable into either a hub/switch if you want another hard wired connection or another wifi access point.
EG
http://www.argos.co.uk/static/Product/partNumber/5650307/Trail/searchtext%3ENETWORK.htm#pdpFullProductInformation