Hi, I've been reading several threads on the forums and askubuntu about people having the same issue as me, which is unstable and slow wifi with the Realtek rtl8188ce wifi adapter. None of the threads have helped.
I am new to Linux, so I can't tell if you in words what I've tried, but if you suggest a terminal command I may recognize it! I can tell you that I've tried the latest official Realtek driver, and it didn't change a thing.

The router I am connected to only supports g and b, not N.

Please let me know if you need more info than this, thanks:

Lenovo Thinkpad L430 L2N36MD
Ubuntu 12.04 LTS 64-bit
Kernel/architecture (including 32 vs. 64 bit):
$ uname -mr
3.2.0-26-generic x86_64
Wireless Brand, Model and Wireless Chipset:
$ lspci | grep Network
06:00.0 Network controller: Realtek Semiconductor Co., Ltd. RTL8188CE 802.11b/g/n WiFi Adapter (rev 01)
$ iwconfig wlan0
wlan0     IEEE 802.11bgn  ESSID:"Fullrate"  
          Mode:Managed  Frequency:2.437 GHz  Access Point: 00:19:CB:E7:09:C5   
          Bit Rate=1 Mb/s   Tx-Power=20 dBm   
          Retry  long limit:7   RTS thr=2347 B   Fragment thr:off
          Power Management:off
          Link Quality=56/70  Signal level=-54 dBm  
          Rx invalid nwid:0  Rx invalid crypt:0  Rx invalid frag:0
          Tx excessive retries:0  Invalid misc:52   Missed beacon:0
$ lsmod | grep 8192
rtl8192ce             137448  0 
rtlwifi               118718  1 rtl8192ce
mac80211              506816  2 rtl8192ce,rtlwifi
Kernel boot messages:
$ dmesg | grep 8192
[    0.000000] PERCPU: Embedded 28 pages/cpu @ffff88011f200000 s83072 r8192 d23424 u262144
[    0.000000] pcpu-alloc: s83072 r8192 d23424 u262144 alloc=1*2097152
[    2.923992] rtl8192ce 0000:06:00.0: PCI INT A -> GSI 17 (level, low) -> IRQ 17
[    2.924006] rtl8192ce 0000:06:00.0: setting latency timer to 64
Network configuration:
$ sudo lshw -C network
       description: Wireless interface
       product: RTL8188CE 802.11b/g/n WiFi Adapter
       vendor: Realtek Semiconductor Co., Ltd.
       physical id: 0
       bus info: pci@0000:06:00.0
       logical name: wlan0
       version: 01
       serial: 7c:e9:d3:f3:b0:e7
       width: 64 bits
       clock: 33MHz
       capabilities: pm msi pciexpress bus_master cap_list ethernet physical wireless
       configuration: broadcast=yes driver=rtl8192ce driverversion=3.2.0-26-generic firmware=N/A ip= latency=0 link=yes multicast=yes wireless=IEEE 802.11bgn
       resources: irq:17 ioport:3000(size=256) memory:f1d00000-f1d03fff
Scan for networks:
$ iwlist scan
wlan0     Scan completed :
          Cell 01 - Address: 00:19:CB:E7:09:C5
                    Frequency:2.437 GHz (Channel 6)
                    Quality=50/70  Signal level=-60 dBm  
                    Encryption key:off
                    Bit Rates:1 Mb/s; 2 Mb/s; 5.5 Mb/s; 11 Mb/s; 22 Mb/s
                    Bit Rates:6 Mb/s; 9 Mb/s; 12 Mb/s; 18 Mb/s; 24 Mb/s
                              36 Mb/s; 48 Mb/s; 54 Mb/s
                    Extra: Last beacon: 12368ms ago
                    IE: Unknown: 000846756C6C72617465
                    IE: Unknown: 010582848B962C
                    IE: Unknown: 030106
                    IE: Unknown: 2A0100
                    IE: Unknown: 32080C1218243048606C