I need a silent, tiny computer which I would use as an SVN and LAMP server (only for development at home, not as a production environment).
I need RAID 1 to ensure the safety of my data.
Could you please recommend a solution?
I'm pretty sure most machines like the eee-box models only have room for the one drive. You can get low power (usually Atom based) machines in larger cases but these are probably bigger than you are looking for.
If you are not adverse to making you own little box you could get a mini-ITX case and motherboard plus a pair of 2.5" drives (spinning disk or SSD) & some RAM and Bob's your uncle. Something like this motherboard and this case would be fairly cheap - prices of such things seem to have fallen since last time I checked so I might have to consider this next time I renew my little home server (with mobo+cpu+case+psu costing that little, the whole build should cheaper than a less well specified eee-box or similar). If you might need more than two drives later down the line (without the drives needing to be being external and connected via USB or LAN) you'll need something a bit chunkier like this motherboard (four SATA ports instead of just two) and this case (which will also take 3.5" drives). If you need more power you can get beefier CPUs on mITX boards, like a core2duo, but be very careful about PSU ratings and CPU cooling if you go that way. A true-dual-core Atom with passive cooling (as seen on the boards I linked to above) should be more than sufficient for the use you describe and will give you much fewer power, heat, and noise concerns than a more power-full & power-hungry CPU would - and it'll be cheaper too. There are a large number of mITX boards and cases out there so you should be able to find a combination that fits your needs and budget.
You might even find good pre-made mITX machines but there were not at my regular supplier to link to at the moment. Most off-the-shelf units will be one drive only meaning you'll have to get your hands dirty at some point anyway so your own build may be the better way to go if you are comfortable with that task - you get the flexibility of choosing all your parts such as you preferred type+manufacturer of drive.
Raid and mini machines do not really go as they usually use smaller laptop grade drives (for noise, power and size)
I recommend that you either get any mini PC then buy yourself a USB Raid box / NAS that supports RAID - Click here for example.
Alternatively, if you are only going to use this for development / testing, have you thought about virtualising your current machine and taking regular backups? This could be a much more cost effective solution.