I'm running a low-end linux myself at home for years, with surprisingly similar characteristics (no FPU either):

    lloeki@slug> cat /proc/cpuinfo                                                ~
    Processor   : XScale-IXP42x Family rev 1 (v5l)
    BogoMIPS    : 266.24
    Features    : swp half thumb fastmult edsp 
    CPU implementer : 0x69
    CPU architecture: 5TE
    CPU variant : 0x0
    CPU part    : 0x41f
    CPU revision    : 1

    Hardware    : Linksys NSLU2
    Revision    : 0000
    Serial      : 0000000000000000
    lloeki@slug> free                                                             ~
                total       used       free     shared    buffers     cached
    Mem:         28844      27212       1632          0       2372      10496
    -/+ buffers/cache:      14344      14500
    Swap:       121076      10272     110804
    lloeki@slug> cat /etc/debian_version                                          ~
    6.0.2

It has been tasked to do quite a bit of things, including:

    - imap+smtp server (smarthost)
    - out-of-cloud mail mirror
    - having a permanent, "immutable" diagnostics access point
    - securing untrusted wifi connexions with a vpn
    - tunnelling through even the worst http proxies (httptunnel+openvpn)
    - hosting a sixxs tunnel and a radvd instance for my LAN
    - IPv6 everywhere (via the openvpn TAP if)
    - NAS
    - networked Linux rsync hardlink delta backup (Time Machine style)
    - private file sharing (kinda like megaupload/dropbox links...)
    - mpd host
    - DNLA server
    - WOL packet sender
    - ssh hop
    - alarm system (cron+aplay)
    - LAN DNS
    - mDNS/dns-sd
    - WAN v4/v6 uptime monitor with history

Debian/arm provides a huuuge number of packages. The biggest constraint is actually not the CPU but the RAM, 2x or 4x that amount would be nice.

Many of those have been phased out when I replaced my wrt54g (v5, dd-wrt) with a Time Capsule, but it saved (and still saves) me time (or even my ass) quite a lot.

Total cost: ~100€ + 5W max. Well worth it.